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Fibonacci polynomials $F_n$
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Numbers
$n$ 
$F_n(x)$
0:
0
1:
1
2:
x
3:
x^2 + 1
4:
x^3 + 2*x
5:
x^4 + 3*x^2 + 1
6:
x^5 + 4*x^3 + 3*x
7:
x^6 + 5*x^4 + 6*x^2 + 1
8:
x^7 + 6*x^5 + 10*x^3 + 4*x
9:
x^8 + 7*x^6 + 15*x^4 + 10*x^2 + 1
10:
x^9 + 8*x^7 + 21*x^5 + 20*x^3 + 5*x
11:
x^10 + 9*x^8 + 28*x^6 + 35*x^4 + 15*x^2 + 1
12:
x^11 + 10*x^9 + 36*x^7 + 56*x^5 + 35*x^3 + 6*x
13:
x^12 + 11*x^10 + 45*x^8 + 84*x^6 + 70*x^4 + 21*x^2 + 1
14:
x^13 + 12*x^11 + 55*x^9 + 120*x^7 + 126*x^5 + 56*x^3 + 7*x
15:
x^14 + 13*x^12 + 66*x^10 + 165*x^8 + 210*x^6 + 126*x^4 + 28*x^2 + 1
16:
x^15 + 14*x^13 + 78*x^11 + 220*x^9 + 330*x^7 + 252*x^5 + 84*x^3 + 8*x
17:
x^16 + 15*x^14 + 91*x^12 + 286*x^10 + 495*x^8 + 462*x^6 + 210*x^4 + 36*x^2 + 1
18:
x^17 + 16*x^15 + 105*x^13 + 364*x^11 + 715*x^9 + 792*x^7 + 462*x^5 + 120*x^3 + 9*x
19:
x^18 + 17*x^16 + 120*x^14 + 455*x^12 + 1001*x^10 + 1287*x^8 + 924*x^6 + 330*x^4 + 45*x^2 + 1
20:
x^19 + 18*x^17 + 136*x^15 + 560*x^13 + 1365*x^11 + 2002*x^9 + 1716*x^7 + 792*x^5 + 165*x^3 + 10*x
21:
x^20 + 19*x^18 + 153*x^16 + 680*x^14 + 1820*x^12 + 3003*x^10 + 3003*x^8 + 1716*x^6 + 495*x^4 + 55*x^2 + 1
22:
x^21 + 20*x^19 + 171*x^17 + 816*x^15 + 2380*x^13 + 4368*x^11 + 5005*x^9 + 3432*x^7 + 1287*x^5 + 220*x^3 + 11*x
23:
x^22 + 21*x^20 + 190*x^18 + 969*x^16 + 3060*x^14 + 6188*x^12 + 8008*x^10 + 6435*x^8 + 3003*x^6 + 715*x^4 + 66*x^2 + 1
24:
x^23 + 22*x^21 + 210*x^19 + 1140*x^17 + 3876*x^15 + 8568*x^13 + 12376*x^11 + 11440*x^9 + 6435*x^7 + 2002*x^5 + 286*x^3 + 12*x
25:
x^24 + 23*x^22 + 231*x^20 + 1330*x^18 + 4845*x^16 + 11628*x^14 + 18564*x^12 + 19448*x^10 + 12870*x^8 + 5005*x^6 + 1001*x^4 + 78*x^2 + 1
26:
x^25 + 24*x^23 + 253*x^21 + 1540*x^19 + 5985*x^17 + 15504*x^15 + 27132*x^13 + 31824*x^11 + 24310*x^9 + 11440*x^7 + 3003*x^5 + 364*x^3 + 13*x
27:
x^26 + 25*x^24 + 276*x^22 + 1771*x^20 + 7315*x^18 + 20349*x^16 + 38760*x^14 + 50388*x^12 + 43758*x^10 + 24310*x^8 + 8008*x^6 + 1365*x^4 + 91*x^2 + 1
28:
x^27 + 26*x^25 + 300*x^23 + 2024*x^21 + 8855*x^19 + 26334*x^17 + 54264*x^15 + 77520*x^13 + 75582*x^11 + 48620*x^9 + 19448*x^7 + 4368*x^5 + 455*x^3 + 14*x
29:
x^28 + 27*x^26 + 325*x^24 + 2300*x^22 + 10626*x^20 + 33649*x^18 + 74613*x^16 + 116280*x^14 + 125970*x^12 + 92378*x^10 + 43758*x^8 + 12376*x^6 + 1820*x^4 + 105*x^2 + 1
30:
x^29 + 28*x^27 + 351*x^25 + 2600*x^23 + 12650*x^21 + 42504*x^19 + 100947*x^17 + 170544*x^15 + 203490*x^13 + 167960*x^11 + 92378*x^9 + 31824*x^7 + 6188*x^5 + 560*x^3 + 15*x
31:
x^30 + 29*x^28 + 378*x^26 + 2925*x^24 + 14950*x^22 + 53130*x^20 + 134596*x^18 + 245157*x^16 + 319770*x^14 + 293930*x^12 + 184756*x^10 + 75582*x^8 + 18564*x^6 + 2380*x^4 + 120*x^2 + 1
32:
x^31 + 30*x^29 + 406*x^27 + 3276*x^25 + 17550*x^23 + 65780*x^21 + 177100*x^19 + 346104*x^17 + 490314*x^15 + 497420*x^13 + 352716*x^11 + 167960*x^9 + 50388*x^7 + 8568*x^5 + 680*x^3 + 16*x
33:
x^32 + 31*x^30 + 435*x^28 + 3654*x^26 + 20475*x^24 + 80730*x^22 + 230230*x^20 + 480700*x^18 + 735471*x^16 + 817190*x^14 + 646646*x^12 + 352716*x^10 + 125970*x^8 + 27132*x^6 + 3060*x^4 + 136*x^2 + 1
34:
x^33 + 32*x^31 + 465*x^29 + 4060*x^27 + 23751*x^25 + 98280*x^23 + 296010*x^21 + 657800*x^19 + 1081575*x^17 + 1307504*x^15 + 1144066*x^13 + 705432*x^11 + 293930*x^9 + 77520*x^7 + 11628*x^5 + 816*x^3 + 17*x
35:
x^34 + 33*x^32 + 496*x^30 + 4495*x^28 + 27405*x^26 + 118755*x^24 + 376740*x^22 + 888030*x^20 + 1562275*x^18 + 2042975*x^16 + 1961256*x^14 + 1352078*x^12 + 646646*x^10 + 203490*x^8 + 38760*x^6 + 3876*x^4 + 153*x^2 + 1
36:
x^35 + 34*x^33 + 528*x^31 + 4960*x^29 + 31465*x^27 + 142506*x^25 + 475020*x^23 + 1184040*x^21 + 2220075*x^19 + 3124550*x^17 + 3268760*x^15 + 2496144*x^13 + 1352078*x^11 + 497420*x^9 + 116280*x^7 + 15504*x^5 + 969*x^3 + 18*x
37:
x^36 + 35*x^34 + 561*x^32 + 5456*x^30 + 35960*x^28 + 169911*x^26 + 593775*x^24 + 1560780*x^22 + 3108105*x^20 + 4686825*x^18 + 5311735*x^16 + 4457400*x^14 + 2704156*x^12 + 1144066*x^10 + 319770*x^8 + 54264*x^6 + 4845*x^4 + 171*x^2 + 1
38:
x^37 + 36*x^35 + 595*x^33 + 5984*x^31 + 40920*x^29 + 201376*x^27 + 736281*x^25 + 2035800*x^23 + 4292145*x^21 + 6906900*x^19 + 8436285*x^17 + 7726160*x^15 + 5200300*x^13 + 2496144*x^11 + 817190*x^9 + 170544*x^7 + 20349*x^5 + 1140*x^3 + 19*x
39:
x^38 + 37*x^36 + 630*x^34 + 6545*x^32 + 46376*x^30 + 237336*x^28 + 906192*x^26 + 2629575*x^24 + 5852925*x^22 + 10015005*x^20 + 13123110*x^18 + 13037895*x^16 + 9657700*x^14 + 5200300*x^12 + 1961256*x^10 + 490314*x^8 + 74613*x^6 + 5985*x^4 + 190*x^2 + 1
40:
x^39 + 38*x^37 + 666*x^35 + 7140*x^33 + 52360*x^31 + 278256*x^29 + 1107568*x^27 + 3365856*x^25 + 7888725*x^23 + 14307150*x^21 + 20030010*x^19 + 21474180*x^17 + 17383860*x^15 + 10400600*x^13 + 4457400*x^11 + 1307504*x^9 + 245157*x^7 + 26334*x^5 + 1330*x^3 + 20*x
41:
x^40 + 39*x^38 + 703*x^36 + 7770*x^34 + 58905*x^32 + 324632*x^30 + 1344904*x^28 + 4272048*x^26 + 10518300*x^24 + 20160075*x^22 + 30045015*x^20 + 34597290*x^18 + 30421755*x^16 + 20058300*x^14 + 9657700*x^12 + 3268760*x^10 + 735471*x^8 + 100947*x^6 + 7315*x^4 + 210*x^2 + 1
42:
x^41 + 40*x^39 + 741*x^37 + 8436*x^35 + 66045*x^33 + 376992*x^31 + 1623160*x^29 + 5379616*x^27 + 13884156*x^25 + 28048800*x^23 + 44352165*x^21 + 54627300*x^19 + 51895935*x^17 + 37442160*x^15 + 20058300*x^13 + 7726160*x^11 + 2042975*x^9 + 346104*x^7 + 33649*x^5 + 1540*x^3 + 21*x
43:
x^42 + 41*x^40 + 780*x^38 + 9139*x^36 + 73815*x^34 + 435897*x^32 + 1947792*x^30 + 6724520*x^28 + 18156204*x^26 + 38567100*x^24 + 64512240*x^22 + 84672315*x^20 + 86493225*x^18 + 67863915*x^16 + 40116600*x^14 + 17383860*x^12 + 5311735*x^10 + 1081575*x^8 + 134596*x^6 + 8855*x^4 + 231*x^2 + 1
44:
x^43 + 42*x^41 + 820*x^39 + 9880*x^37 + 82251*x^35 + 501942*x^33 + 2324784*x^31 + 8347680*x^29 + 23535820*x^27 + 52451256*x^25 + 92561040*x^23 + 129024480*x^21 + 141120525*x^19 + 119759850*x^17 + 77558760*x^15 + 37442160*x^13 + 13037895*x^11 + 3124550*x^9 + 480700*x^7 + 42504*x^5 + 1771*x^3 + 22*x
45:
x^44 + 43*x^42 + 861*x^40 + 10660*x^38 + 91390*x^36 + 575757*x^34 + 2760681*x^32 + 10295472*x^30 + 30260340*x^28 + 70607460*x^26 + 131128140*x^24 + 193536720*x^22 + 225792840*x^20 + 206253075*x^18 + 145422675*x^16 + 77558760*x^14 + 30421755*x^12 + 8436285*x^10 + 1562275*x^8 + 177100*x^6 + 10626*x^4 + 253*x^2 + 1
46:
x^45 + 44*x^43 + 903*x^41 + 11480*x^39 + 101270*x^37 + 658008*x^35 + 3262623*x^33 + 12620256*x^31 + 38608020*x^29 + 94143280*x^27 + 183579396*x^25 + 286097760*x^23 + 354817320*x^21 + 347373600*x^19 + 265182525*x^17 + 155117520*x^15 + 67863915*x^13 + 21474180*x^11 + 4686825*x^9 + 657800*x^7 + 53130*x^5 + 2024*x^3 + 23*x
47:
x^46 + 45*x^44 + 946*x^42 + 12341*x^40 + 111930*x^38 + 749398*x^36 + 3838380*x^34 + 15380937*x^32 + 48903492*x^30 + 124403620*x^28 + 254186856*x^26 + 417225900*x^24 + 548354040*x^22 + 573166440*x^20 + 471435600*x^18 + 300540195*x^16 + 145422675*x^14 + 51895935*x^12 + 13123110*x^10 + 2220075*x^8 + 230230*x^6 + 12650*x^4 + 276*x^2 + 1
48:
x^47 + 46*x^45 + 990*x^43 + 13244*x^41 + 123410*x^39 + 850668*x^37 + 4496388*x^35 + 18643560*x^33 + 61523748*x^31 + 163011640*x^29 + 348330136*x^27 + 600805296*x^25 + 834451800*x^23 + 927983760*x^21 + 818809200*x^19 + 565722720*x^17 + 300540195*x^15 + 119759850*x^13 + 34597290*x^11 + 6906900*x^9 + 888030*x^7 + 65780*x^5 + 2300*x^3 + 24*x
49:
x^48 + 47*x^46 + 1035*x^44 + 14190*x^42 + 135751*x^40 + 962598*x^38 + 5245786*x^36 + 22481940*x^34 + 76904685*x^32 + 211915132*x^30 + 472733756*x^28 + 854992152*x^26 + 1251677700*x^24 + 1476337800*x^22 + 1391975640*x^20 + 1037158320*x^18 + 601080390*x^16 + 265182525*x^14 + 86493225*x^12 + 20030010*x^10 + 3108105*x^8 + 296010*x^6 + 14950*x^4 + 300*x^2 + 1
50:
x^49 + 48*x^47 + 1081*x^45 + 15180*x^43 + 148995*x^41 + 1086008*x^39 + 6096454*x^37 + 26978328*x^35 + 95548245*x^33 + 273438880*x^31 + 635745396*x^29 + 1203322288*x^27 + 1852482996*x^25 + 2310789600*x^23 + 2319959400*x^21 + 1855967520*x^19 + 1166803110*x^17 + 565722720*x^15 + 206253075*x^13 + 54627300*x^11 + 10015005*x^9 + 1184040*x^7 + 80730*x^5 + 2600*x^3 + 25*x
51:
x^50 + 49*x^48 + 1128*x^46 + 16215*x^44 + 163185*x^42 + 1221759*x^40 + 7059052*x^38 + 32224114*x^36 + 118030185*x^34 + 350343565*x^32 + 847660528*x^30 + 1676056044*x^28 + 2707475148*x^26 + 3562467300*x^24 + 3796297200*x^22 + 3247943160*x^20 + 2203961430*x^18 + 1166803110*x^16 + 471435600*x^14 + 141120525*x^12 + 30045015*x^10 + 4292145*x^8 + 376740*x^6 + 17550*x^4 + 325*x^2 + 1
52:
x^51 + 50*x^49 + 1176*x^47 + 17296*x^45 + 178365*x^43 + 1370754*x^41 + 8145060*x^39 + 38320568*x^37 + 145008513*x^35 + 445891810*x^33 + 1121099408*x^31 + 2311801440*x^29 + 3910797436*x^27 + 5414950296*x^25 + 6107086800*x^23 + 5567902560*x^21 + 4059928950*x^19 + 2333606220*x^17 + 1037158320*x^15 + 347373600*x^13 + 84672315*x^11 + 14307150*x^9 + 1560780*x^7 + 98280*x^5 + 2925*x^3 + 26*x
53:
x^52 + 51*x^50 + 1225*x^48 + 18424*x^46 + 194580*x^44 + 1533939*x^42 + 9366819*x^40 + 45379620*x^38 + 177232627*x^36 + 563921995*x^34 + 1471442973*x^32 + 3159461968*x^30 + 5586853480*x^28 + 8122425444*x^26 + 9669554100*x^24 + 9364199760*x^22 + 7307872110*x^20 + 4537567650*x^18 + 2203961430*x^16 + 818809200*x^14 + 225792840*x^12 + 44352165*x^10 + 5852925*x^8 + 475020*x^6 + 20475*x^4 + 351*x^2 + 1
54:
x^53 + 52*x^51 + 1275*x^49 + 19600*x^47 + 211876*x^45 + 1712304*x^43 + 10737573*x^41 + 53524680*x^39 + 215553195*x^37 + 708930508*x^35 + 1917334783*x^33 + 4280561376*x^31 + 7898654920*x^29 + 12033222880*x^27 + 15084504396*x^25 + 15471286560*x^23 + 12875774670*x^21 + 8597496600*x^19 + 4537567650*x^17 + 1855967520*x^15 + 573166440*x^13 + 129024480*x^11 + 20160075*x^9 + 2035800*x^7 + 118755*x^5 + 3276*x^3 + 27*x
55:
x^54 + 53*x^52 + 1326*x^50 + 20825*x^48 + 230300*x^46 + 1906884*x^44 + 12271512*x^42 + 62891499*x^40 + 260932815*x^38 + 886163135*x^36 + 2481256778*x^34 + 5752004349*x^32 + 11058116888*x^30 + 17620076360*x^28 + 23206929840*x^26 + 25140840660*x^24 + 22239974430*x^22 + 15905368710*x^20 + 9075135300*x^18 + 4059928950*x^16 + 1391975640*x^14 + 354817320*x^12 + 64512240*x^10 + 7888725*x^8 + 593775*x^6 + 23751*x^4 + 378*x^2 + 1
56:
x^55 + 54*x^53 + 1378*x^51 + 22100*x^49 + 249900*x^47 + 2118760*x^45 + 13983816*x^43 + 73629072*x^41 + 314457495*x^39 + 1101716330*x^37 + 3190187286*x^35 + 7669339132*x^33 + 15338678264*x^31 + 25518731280*x^29 + 35240152720*x^27 + 40225345056*x^25 + 37711260990*x^23 + 28781143380*x^21 + 17672631900*x^19 + 8597496600*x^17 + 3247943160*x^15 + 927983760*x^13 + 193536720*x^11 + 28048800*x^9 + 2629575*x^7 + 142506*x^5 + 3654*x^3 + 28*x
57:
x^56 + 55*x^54 + 1431*x^52 + 23426*x^50 + 270725*x^48 + 2349060*x^46 + 15890700*x^44 + 85900584*x^42 + 377348994*x^40 + 1362649145*x^38 + 4076350421*x^36 + 10150595910*x^34 + 21090682613*x^32 + 36576848168*x^30 + 52860229080*x^28 + 63432274896*x^26 + 62852101650*x^24 + 51021117810*x^22 + 33578000610*x^20 + 17672631900*x^18 + 7307872110*x^16 + 2319959400*x^14 + 548354040*x^12 + 92561040*x^10 + 10518300*x^8 + 736281*x^6 + 27405*x^4 + 406*x^2 + 1
58:
x^57 + 56*x^55 + 1485*x^53 + 24804*x^51 + 292825*x^49 + 2598960*x^47 + 18009460*x^45 + 99884400*x^43 + 450978066*x^41 + 1677106640*x^39 + 5178066751*x^37 + 13340783196*x^35 + 28760021745*x^33 + 51915526432*x^31 + 78378960360*x^29 + 98672427616*x^27 + 103077446706*x^25 + 88732378800*x^23 + 62359143990*x^21 + 35345263800*x^19 + 15905368710*x^17 + 5567902560*x^15 + 1476337800*x^13 + 286097760*x^11 + 38567100*x^9 + 3365856*x^7 + 169911*x^5 + 4060*x^3 + 29*x
59:
x^58 + 57*x^56 + 1540*x^54 + 26235*x^52 + 316251*x^50 + 2869685*x^48 + 20358520*x^46 + 115775100*x^44 + 536878650*x^42 + 2054455634*x^40 + 6540715896*x^38 + 17417133617*x^36 + 38910617655*x^34 + 73006209045*x^32 + 114955808528*x^30 + 151532656696*x^28 + 166509721602*x^26 + 151584480450*x^24 + 113380261800*x^22 + 68923264410*x^20 + 33578000610*x^18 + 12875774670*x^16 + 3796297200*x^14 + 834451800*x^12 + 131128140*x^10 + 13884156*x^8 + 906192*x^6 + 31465*x^4 + 435*x^2 + 1
60:
x^59 + 58*x^57 + 1596*x^55 + 27720*x^53 + 341055*x^51 + 3162510*x^49 + 22957480*x^47 + 133784560*x^45 + 636763050*x^43 + 2505433700*x^41 + 8217822536*x^39 + 22595200368*x^37 + 52251400851*x^35 + 101766230790*x^33 + 166871334960*x^31 + 229911617056*x^29 + 265182149218*x^27 + 254661927156*x^25 + 202112640600*x^23 + 131282408400*x^21 + 68923264410*x^19 + 28781143380*x^17 + 9364199760*x^15 + 2310789600*x^13 + 417225900*x^11 + 52451256*x^9 + 4272048*x^7 + 201376*x^5 + 4495*x^3 + 30*x
61:
x^60 + 59*x^58 + 1653*x^56 + 29260*x^54 + 367290*x^52 + 3478761*x^50 + 25827165*x^48 + 154143080*x^46 + 752538150*x^44 + 3042312350*x^42 + 10272278170*x^40 + 29135916264*x^38 + 69668534468*x^36 + 140676848445*x^34 + 239877544005*x^32 + 344867425584*x^30 + 416714805914*x^28 + 421171648758*x^26 + 353697121050*x^24 + 244662670200*x^22 + 137846528820*x^20 + 62359143990*x^18 + 22239974430*x^16 + 6107086800*x^14 + 1251677700*x^12 + 183579396*x^10 + 18156204*x^8 + 1107568*x^6 + 35960*x^4 + 465*x^2 + 1
62:
x^61 + 60*x^59 + 1711*x^57 + 30856*x^55 + 395010*x^53 + 3819816*x^51 + 28989675*x^49 + 177100560*x^47 + 886322710*x^45 + 3679075400*x^43 + 12777711870*x^41 + 37353738800*x^39 + 92263734836*x^37 + 192928249296*x^35 + 341643774795*x^33 + 511738760544*x^31 + 646626422970*x^29 + 686353797976*x^27 + 608359048206*x^25 + 446775310800*x^23 + 269128937220*x^21 + 131282408400*x^19 + 51021117810*x^17 + 15471286560*x^15 + 3562467300*x^13 + 600805296*x^11 + 70607460*x^9 + 5379616*x^7 + 237336*x^5 + 4960*x^3 + 31*x
63:
x^62 + 61*x^60 + 1770*x^58 + 32509*x^56 + 424270*x^54 + 4187106*x^52 + 32468436*x^50 + 202927725*x^48 + 1040465790*x^46 + 4431613550*x^44 + 15820024220*x^42 + 47626016970*x^40 + 121399651100*x^38 + 262596783764*x^36 + 482320623240*x^34 + 751616304549*x^32 + 991493848554*x^30 + 1103068603890*x^28 + 1029530696964*x^26 + 800472431850*x^24 + 513791607420*x^22 + 269128937220*x^20 + 113380261800*x^18 + 37711260990*x^16 + 9669554100*x^14 + 1852482996*x^12 + 254186856*x^10 + 23535820*x^8 + 1344904*x^6 + 40920*x^4 + 496*x^2 + 1
64:
x^63 + 62*x^61 + 1830*x^59 + 34220*x^57 + 455126*x^55 + 4582116*x^53 + 36288252*x^51 + 231917400*x^49 + 1217566350*x^47 + 5317936260*x^45 + 19499099620*x^43 + 60403728840*x^41 + 158753389900*x^39 + 354860518600*x^37 + 675248872536*x^35 + 1093260079344*x^33 + 1503232609098*x^31 + 1749695026860*x^29 + 1715884494940*x^27 + 1408831480056*x^25 + 960566918220*x^23 + 538257874440*x^21 + 244662670200*x^19 + 88732378800*x^17 + 25140840660*x^15 + 5414950296*x^13 + 854992152*x^11 + 94143280*x^9 + 6724520*x^7 + 278256*x^5 + 5456*x^3 + 32*x
65:
x^64 + 63*x^62 + 1891*x^60 + 35990*x^58 + 487635*x^56 + 5006386*x^54 + 40475358*x^52 + 264385836*x^50 + 1420494075*x^48 + 6358402050*x^46 + 23930713170*x^44 + 76223753060*x^42 + 206379406870*x^40 + 476260169700*x^38 + 937845656300*x^36 + 1575580702584*x^34 + 2254848913647*x^32 + 2741188875414*x^30 + 2818953098830*x^28 + 2438362177020*x^26 + 1761039350070*x^24 + 1052049481860*x^22 + 513791607420*x^20 + 202112640600*x^18 + 62852101650*x^16 + 15084504396*x^14 + 2707475148*x^12 + 348330136*x^10 + 30260340*x^8 + 1623160*x^6 + 46376*x^4 + 528*x^2 + 1
66:
x^65 + 64*x^63 + 1953*x^61 + 37820*x^59 + 521855*x^57 + 5461512*x^55 + 45057474*x^53 + 300674088*x^51 + 1652411475*x^49 + 7575968400*x^47 + 29248649430*x^45 + 95722852680*x^43 + 266783135710*x^41 + 635013559600*x^39 + 1292706174900*x^37 + 2250829575120*x^35 + 3348108992991*x^33 + 4244421484512*x^31 + 4568648125690*x^29 + 4154246671960*x^27 + 3169870830126*x^25 + 2012616400080*x^23 + 1052049481860*x^21 + 446775310800*x^19 + 151584480450*x^17 + 40225345056*x^15 + 8122425444*x^13 + 1203322288*x^11 + 124403620*x^9 + 8347680*x^7 + 324632*x^5 + 5984*x^3 + 33*x
67:
x^66 + 65*x^64 + 2016*x^62 + 39711*x^60 + 557845*x^58 + 5949147*x^56 + 50063860*x^54 + 341149446*x^52 + 1916797311*x^50 + 8996462475*x^48 + 35607051480*x^46 + 119653565850*x^44 + 343006888770*x^42 + 841392966470*x^40 + 1768966344600*x^38 + 3188675231420*x^36 + 4923689695575*x^34 + 6499270398159*x^32 + 7309837001104*x^30 + 6973199770790*x^28 + 5608233007146*x^26 + 3773655750150*x^24 + 2104098963720*x^22 + 960566918220*x^20 + 353697121050*x^18 + 103077446706*x^16 + 23206929840*x^14 + 3910797436*x^12 + 472733756*x^10 + 38608020*x^8 + 1947792*x^6 + 52360*x^4 + 561*x^2 + 1
68:
x^67 + 66*x^65 + 2080*x^63 + 41664*x^61 + 595665*x^59 + 6471002*x^57 + 55525372*x^55 + 386206920*x^53 + 2217471399*x^51 + 10648873950*x^49 + 43183019880*x^47 + 148902215280*x^45 + 438729741450*x^43 + 1108176102180*x^41 + 2403979904200*x^39 + 4481381406320*x^37 + 7174519270695*x^35 + 9847379391150*x^33 + 11554258485616*x^31 + 11541847896480*x^29 + 9762479679106*x^27 + 6943526580276*x^25 + 4116715363800*x^23 + 2012616400080*x^21 + 800472431850*x^19 + 254661927156*x^17 + 63432274896*x^15 + 12033222880*x^13 + 1676056044*x^11 + 163011640*x^9 + 10295472*x^7 + 376992*x^5 + 6545*x^3 + 34*x
69:
x^68 + 67*x^66 + 2145*x^64 + 43680*x^62 + 635376*x^60 + 7028847*x^58 + 61474519*x^56 + 436270780*x^54 + 2558620845*x^52 + 12565671261*x^50 + 52179482355*x^48 + 184509266760*x^46 + 558383307300*x^44 + 1451182990950*x^42 + 3245372870670*x^40 + 6250347750920*x^38 + 10363194502115*x^36 + 14771069086725*x^34 + 18053528883775*x^32 + 18851684897584*x^30 + 16735679449896*x^28 + 12551759587422*x^26 + 7890371113950*x^24 + 4116715363800*x^22 + 1761039350070*x^20 + 608359048206*x^18 + 166509721602*x^16 + 35240152720*x^14 + 5586853480*x^12 + 635745396*x^10 + 48903492*x^8 + 2324784*x^6 + 58905*x^4 + 595*x^2 + 1
70:
x^69 + 68*x^67 + 2211*x^65 + 45760*x^63 + 677040*x^61 + 7624512*x^59 + 67945521*x^57 + 491796152*x^55 + 2944827765*x^53 + 14783142660*x^51 + 62828356305*x^49 + 227692286640*x^47 + 707285522580*x^45 + 1889912732400*x^43 + 4353548972850*x^41 + 8654327655120*x^39 + 14844575908435*x^37 + 21945588357420*x^35 + 27900908274925*x^33 + 30405943383200*x^31 + 28277527346376*x^29 + 22314239266528*x^27 + 14833897694226*x^25 + 8233430727600*x^23 + 3773655750150*x^21 + 1408831480056*x^19 + 421171648758*x^17 + 98672427616*x^15 + 17620076360*x^13 + 2311801440*x^11 + 211915132*x^9 + 12620256*x^7 + 435897*x^5 + 7140*x^3 + 35*x
71:
x^70 + 69*x^68 + 2278*x^66 + 47905*x^64 + 720720*x^62 + 8259888*x^60 + 74974368*x^58 + 553270671*x^56 + 3381098545*x^54 + 17341763505*x^52 + 75394027566*x^50 + 279871768995*x^48 + 891794789340*x^46 + 2448296039700*x^44 + 5804731963800*x^42 + 11899700525790*x^40 + 21094923659355*x^38 + 32308782859535*x^36 + 42671977361650*x^34 + 48459472266975*x^32 + 47129212243960*x^30 + 39049918716424*x^28 + 27385657281648*x^26 + 16123801841550*x^24 + 7890371113950*x^22 + 3169870830126*x^20 + 1029530696964*x^18 + 265182149218*x^16 + 52860229080*x^14 + 7898654920*x^12 + 847660528*x^10 + 61523748*x^8 + 2760681*x^6 + 66045*x^4 + 630*x^2 + 1
72:
x^71 + 70*x^69 + 2346*x^67 + 50116*x^65 + 766480*x^63 + 8936928*x^61 + 82598880*x^59 + 621216192*x^57 + 3872894697*x^55 + 20286591270*x^53 + 90177170226*x^51 + 342700125300*x^49 + 1119487075980*x^47 + 3155581562280*x^45 + 7694644696200*x^43 + 16253249498640*x^41 + 29749251314475*x^39 + 47153358767970*x^37 + 64617565719070*x^35 + 76360380541900*x^33 + 77535155627160*x^31 + 67327446062800*x^29 + 49699896548176*x^27 + 30957699535776*x^25 + 16123801841550*x^23 + 6943526580276*x^21 + 2438362177020*x^19 + 686353797976*x^17 + 151532656696*x^15 + 25518731280*x^13 + 3159461968*x^11 + 273438880*x^9 + 15380937*x^7 + 501942*x^5 + 7770*x^3 + 36*x
73:
x^72 + 71*x^70 + 2415*x^68 + 52394*x^66 + 814385*x^64 + 9657648*x^62 + 90858768*x^60 + 696190560*x^58 + 4426165368*x^56 + 23667689815*x^54 + 107518933731*x^52 + 418094152866*x^50 + 1399358844975*x^48 + 4047376351620*x^46 + 10142940735900*x^44 + 22057981462440*x^42 + 41648951840265*x^40 + 68248282427325*x^38 + 96926348578605*x^36 + 119032357903550*x^34 + 125994627894135*x^32 + 114456658306760*x^30 + 88749815264600*x^28 + 58343356817424*x^26 + 32247603683100*x^24 + 14833897694226*x^22 + 5608233007146*x^20 + 1715884494940*x^18 + 416714805914*x^16 + 78378960360*x^14 + 11058116888*x^12 + 1121099408*x^10 + 76904685*x^8 + 3262623*x^6 + 73815*x^4 + 666*x^2 + 1
74:
x^73 + 72*x^71 + 2485*x^69 + 54740*x^67 + 864501*x^65 + 10424128*x^63 + 99795696*x^61 + 778789440*x^59 + 5047381560*x^57 + 27540584512*x^55 + 127805525001*x^53 + 508271323092*x^51 + 1742058970275*x^49 + 5166863427600*x^47 + 13298522298180*x^45 + 29752626158640*x^43 + 57902201338905*x^41 + 97997533741800*x^39 + 144079707346575*x^37 + 183649923622620*x^35 + 202355008436035*x^33 + 191991813933920*x^31 + 156077261327400*x^29 + 108043253365600*x^27 + 63205303218876*x^25 + 30957699535776*x^23 + 12551759587422*x^21 + 4154246671960*x^19 + 1103068603890*x^17 + 229911617056*x^15 + 36576848168*x^13 + 4280561376*x^11 + 350343565*x^9 + 18643560*x^7 + 575757*x^5 + 8436*x^3 + 37*x
75:
x^74 + 73*x^72 + 2556*x^70 + 57155*x^68 + 916895*x^66 + 11238513*x^64 + 109453344*x^62 + 869648208*x^60 + 5743572120*x^58 + 31966749880*x^56 + 151473214816*x^54 + 615790256823*x^52 + 2160153123141*x^50 + 6566222272575*x^48 + 17345898649800*x^46 + 39895566894540*x^44 + 79960182801345*x^42 + 139646485582065*x^40 + 212327989773900*x^38 + 280576272201225*x^36 + 321387366339585*x^34 + 317986441828055*x^32 + 270533919634160*x^30 + 196793068630200*x^28 + 121548660036300*x^26 + 63205303218876*x^24 + 27385657281648*x^22 + 9762479679106*x^20 + 2818953098830*x^18 + 646626422970*x^16 + 114955808528*x^14 + 15338678264*x^12 + 1471442973*x^10 + 95548245*x^8 + 3838380*x^6 + 82251*x^4 + 703*x^2 + 1
76:
x^75 + 74*x^73 + 2628*x^71 + 59640*x^69 + 971635*x^67 + 12103014*x^65 + 119877472*x^63 + 969443904*x^61 + 6522361560*x^59 + 37014131440*x^57 + 179013799328*x^55 + 743595781824*x^53 + 2668424446233*x^51 + 8308281242850*x^49 + 22512762077400*x^47 + 53194089192720*x^45 + 109712808959985*x^43 + 197548686920970*x^41 + 310325523515700*x^39 + 424655979547800*x^37 + 505037289962205*x^35 + 520341450264090*x^33 + 462525733568080*x^31 + 352870329957600*x^29 + 229591913401900*x^27 + 126410606437752*x^25 + 58343356817424*x^23 + 22314239266528*x^21 + 6973199770790*x^19 + 1749695026860*x^17 + 344867425584*x^15 + 51915526432*x^13 + 5752004349*x^11 + 445891810*x^9 + 22481940*x^7 + 658008*x^5 + 9139*x^3 + 38*x
77:
x^76 + 75*x^74 + 2701*x^72 + 62196*x^70 + 1028790*x^68 + 13019909*x^66 + 131115985*x^64 + 1078897248*x^62 + 7392009768*x^60 + 42757703560*x^58 + 210980549208*x^56 + 895068996640*x^54 + 3284214703056*x^52 + 10468434365991*x^50 + 29078984349975*x^48 + 70539987842520*x^46 + 149608375854525*x^44 + 277508869722315*x^42 + 449972009097765*x^40 + 636983969321700*x^38 + 785613562163430*x^36 + 841728816603675*x^34 + 780512175396135*x^32 + 623404249591760*x^30 + 426384982032100*x^28 + 247959266474052*x^26 + 121548660036300*x^24 + 49699896548176*x^22 + 16735679449896*x^20 + 4568648125690*x^18 + 991493848554*x^16 + 166871334960*x^14 + 21090682613*x^12 + 1917334783*x^10 + 118030185*x^8 + 4496388*x^6 + 91390*x^4 + 741*x^2 + 1
78:
x^77 + 76*x^75 + 2775*x^73 + 64824*x^71 + 1088430*x^69 + 13991544*x^67 + 143218999*x^65 + 1198774720*x^63 + 8361453672*x^61 + 49280065120*x^59 + 247994680648*x^57 + 1074082795968*x^55 + 4027810484880*x^53 + 13136858812224*x^51 + 37387265592825*x^49 + 93052749919920*x^47 + 202802465047245*x^45 + 387221678682300*x^43 + 647520696018735*x^41 + 947309492837400*x^39 + 1210269541711230*x^37 + 1346766106565880*x^35 + 1300853625660225*x^33 + 1085929983159840*x^31 + 779255311989700*x^29 + 477551179875952*x^27 + 247959266474052*x^25 + 108043253365600*x^23 + 39049918716424*x^21 + 11541847896480*x^19 + 2741188875414*x^17 + 511738760544*x^15 + 73006209045*x^13 + 7669339132*x^11 + 563921995*x^9 + 26978328*x^7 + 749398*x^5 + 9880*x^3 + 39*x
79:
x^78 + 77*x^76 + 2850*x^74 + 67525*x^72 + 1150626*x^70 + 15020334*x^68 + 156238908*x^66 + 1329890705*x^64 + 9440350920*x^62 + 56672074888*x^60 + 290752384208*x^58 + 1285063345176*x^56 + 4922879481520*x^54 + 16421073515280*x^52 + 47855699958816*x^50 + 122131734269895*x^48 + 273342452889765*x^46 + 536830054536825*x^44 + 925029565741050*x^42 + 1397281501935165*x^40 + 1847253511032930*x^38 + 2132379668729310*x^36 + 2142582442263900*x^34 + 1866442158555975*x^32 + 1402659561581460*x^30 + 903936161908052*x^28 + 495918532948104*x^26 + 229591913401900*x^24 + 88749815264600*x^22 + 28277527346376*x^20 + 7309837001104*x^18 + 1503232609098*x^16 + 239877544005*x^14 + 28760021745*x^12 + 2481256778*x^10 + 145008513*x^8 + 5245786*x^6 + 101270*x^4 + 780*x^2 + 1
80:
x^79 + 78*x^77 + 2926*x^75 + 70300*x^73 + 1215450*x^71 + 16108764*x^69 + 170230452*x^67 + 1473109704*x^65 + 10639125640*x^63 + 65033528560*x^61 + 340032449328*x^59 + 1533058025824*x^57 + 5996962277488*x^55 + 20448884000160*x^53 + 60992558771040*x^51 + 159518999862720*x^49 + 366395202809685*x^47 + 739632519584070*x^45 + 1312251244423350*x^43 + 2044802197953900*x^41 + 2794563003870330*x^39 + 3342649210440540*x^37 + 3489348548829780*x^35 + 3167295784216200*x^33 + 2488589544741300*x^31 + 1683191473897752*x^29 + 973469712824056*x^27 + 477551179875952*x^25 + 196793068630200*x^23 + 67327446062800*x^21 + 18851684897584*x^19 + 4244421484512*x^17 + 751616304549*x^15 + 101766230790*x^13 + 10150595910*x^11 + 708930508*x^9 + 32224114*x^7 + 850668*x^5 + 10660*x^3 + 40*x
81:
x^80 + 79*x^78 + 3003*x^76 + 73150*x^74 + 1282975*x^72 + 17259390*x^70 + 185250786*x^68 + 1629348612*x^66 + 11969016345*x^64 + 74473879480*x^62 + 396704524216*x^60 + 1823810410032*x^58 + 7282025622664*x^56 + 25371763481680*x^54 + 77413632286320*x^52 + 207374699821536*x^50 + 488526937079580*x^48 + 1012974972473835*x^46 + 1849081298960175*x^44 + 2969831763694950*x^42 + 4191844505805495*x^40 + 5189902721473470*x^38 + 5621728217559090*x^36 + 5309878226480100*x^34 + 4355031703297275*x^32 + 3085851035479212*x^30 + 1877405874732108*x^28 + 973469712824056*x^26 + 426384982032100*x^24 + 156077261327400*x^22 + 47129212243960*x^20 + 11554258485616*x^18 + 2254848913647*x^16 + 341643774795*x^14 + 38910617655*x^12 + 3190187286*x^10 + 177232627*x^8 + 6096454*x^6 + 111930*x^4 + 820*x^2 + 1
82:
x^81 + 80*x^79 + 3081*x^77 + 76076*x^75 + 1353275*x^73 + 18474840*x^71 + 201359550*x^69 + 1799579064*x^67 + 13442126049*x^65 + 85113005120*x^63 + 461738052776*x^61 + 2163842859360*x^59 + 8815083648488*x^57 + 31368725759168*x^55 + 97862516286480*x^53 + 268367258592576*x^51 + 648045936942300*x^49 + 1379370175283520*x^47 + 2588713818544245*x^45 + 4282083008118300*x^43 + 6236646703759395*x^41 + 7984465725343800*x^39 + 8964377427999630*x^37 + 8799226775309880*x^35 + 7522327487513475*x^33 + 5574440580220512*x^31 + 3560597348629860*x^29 + 1946939425648112*x^27 + 903936161908052*x^25 + 352870329957600*x^23 + 114456658306760*x^21 + 30405943383200*x^19 + 6499270398159*x^17 + 1093260079344*x^15 + 140676848445*x^13 + 13340783196*x^11 + 886163135*x^9 + 38320568*x^7 + 962598*x^5 + 11480*x^3 + 41*x
83:
x^82 + 81*x^80 + 3160*x^78 + 79079*x^76 + 1426425*x^74 + 19757815*x^72 + 218618940*x^70 + 1984829850*x^68 + 15071474661*x^66 + 97082021465*x^64 + 536211932256*x^62 + 2560547383576*x^60 + 10638894058520*x^58 + 38650751381832*x^56 + 123234279768160*x^54 + 345780890878896*x^52 + 855420636763836*x^50 + 1867897112363100*x^48 + 3601688791018080*x^46 + 6131164307078475*x^44 + 9206478467454345*x^42 + 12176310231149295*x^40 + 14154280149473100*x^38 + 14420954992868970*x^36 + 12832205713993575*x^34 + 9929472283517787*x^32 + 6646448384109072*x^30 + 3824345300380220*x^28 + 1877405874732108*x^26 + 779255311989700*x^24 + 270533919634160*x^22 + 77535155627160*x^20 + 18053528883775*x^18 + 3348108992991*x^16 + 482320623240*x^14 + 52251400851*x^12 + 4076350421*x^10 + 215553195*x^8 + 7059052*x^6 + 123410*x^4 + 861*x^2 + 1
84:
x^83 + 82*x^81 + 3240*x^79 + 82160*x^77 + 1502501*x^75 + 21111090*x^73 + 237093780*x^71 + 2186189400*x^69 + 16871053725*x^67 + 110524147514*x^65 + 621324937376*x^63 + 3022285436352*x^61 + 12802736917880*x^59 + 47465835030320*x^57 + 154603005527328*x^55 + 443643407165376*x^53 + 1123787895356412*x^51 + 2515943049305400*x^49 + 4981058966301600*x^47 + 8719878125622720*x^45 + 13488561475572645*x^43 + 18412956934908690*x^41 + 22138745874816900*x^39 + 23385332420868600*x^37 + 21631432489303455*x^35 + 17451799771031262*x^33 + 12220888964329584*x^31 + 7384942649010080*x^29 + 3824345300380220*x^27 + 1683191473897752*x^25 + 623404249591760*x^23 + 191991813933920*x^21 + 48459472266975*x^19 + 9847379391150*x^17 + 1575580702584*x^15 + 192928249296*x^13 + 17417133617*x^11 + 1101716330*x^9 + 45379620*x^7 + 1086008*x^5 + 12341*x^3 + 42*x
85:
x^84 + 83*x^82 + 3321*x^80 + 85320*x^78 + 1581580*x^76 + 22537515*x^74 + 256851595*x^72 + 2404808340*x^70 + 18855883575*x^68 + 125595622175*x^66 + 718406958841*x^64 + 3558497368608*x^62 + 15363284301456*x^60 + 58104729088840*x^58 + 193253756909160*x^56 + 566877686933536*x^54 + 1469568786235308*x^52 + 3371363686069236*x^50 + 6848956078664700*x^48 + 12321566916640800*x^46 + 19619725782651120*x^44 + 27619435402363035*x^42 + 34315056105966195*x^40 + 37539612570341700*x^38 + 36052387482172425*x^36 + 30284005485024837*x^34 + 22150361247847371*x^32 + 14031391033119152*x^30 + 7648690600760440*x^28 + 3560597348629860*x^26 + 1402659561581460*x^24 + 462525733568080*x^22 + 125994627894135*x^20 + 27900908274925*x^18 + 4923689695575*x^16 + 675248872536*x^14 + 69668534468*x^12 + 5178066751*x^10 + 260932815*x^8 + 8145060*x^6 + 135751*x^4 + 903*x^2 + 1
86:
x^85 + 84*x^83 + 3403*x^81 + 88560*x^79 + 1663740*x^77 + 24040016*x^75 + 277962685*x^73 + 2641902120*x^71 + 21042072975*x^69 + 142466675900*x^67 + 828931106355*x^65 + 4179822305984*x^63 + 18385569737808*x^61 + 70907466006720*x^59 + 240719591939480*x^57 + 721480692460864*x^55 + 1913212193400684*x^53 + 4495151581425648*x^51 + 9364899127970100*x^49 + 17302625882942400*x^47 + 28339603908273840*x^45 + 41107996877935680*x^43 + 52728013040874885*x^41 + 59678358445158600*x^39 + 59437719903041025*x^37 + 51915437974328292*x^35 + 39602161018878633*x^33 + 26252279997448736*x^31 + 15033633249770520*x^29 + 7384942649010080*x^27 + 3085851035479212*x^25 + 1085929983159840*x^23 + 317986441828055*x^21 + 76360380541900*x^19 + 14771069086725*x^17 + 2250829575120*x^15 + 262596783764*x^13 + 22595200368*x^11 + 1362649145*x^9 + 53524680*x^7 + 1221759*x^5 + 13244*x^3 + 43*x
87:
x^86 + 85*x^84 + 3486*x^82 + 91881*x^80 + 1749060*x^78 + 25621596*x^76 + 300500200*x^74 + 2898753715*x^72 + 23446881315*x^70 + 161322559475*x^68 + 954526728530*x^66 + 4898229264825*x^64 + 21944067106416*x^62 + 86270750308176*x^60 + 298824321028320*x^58 + 914734449370024*x^56 + 2480089880334220*x^54 + 5964720367660956*x^52 + 12736262814039336*x^50 + 24151581961607100*x^48 + 40661170824914640*x^46 + 60727722660586800*x^44 + 80347448443237920*x^42 + 93993414551124795*x^40 + 96977332473382725*x^38 + 87967825456500717*x^36 + 69886166503903470*x^34 + 48402641245296107*x^32 + 29065024282889672*x^30 + 15033633249770520*x^28 + 6646448384109072*x^26 + 2488589544741300*x^24 + 780512175396135*x^22 + 202355008436035*x^20 + 42671977361650*x^18 + 7174519270695*x^16 + 937845656300*x^14 + 92263734836*x^12 + 6540715896*x^10 + 314457495*x^8 + 9366819*x^6 + 148995*x^4 + 946*x^2 + 1
88:
x^87 + 86*x^85 + 3570*x^83 + 95284*x^81 + 1837620*x^79 + 27285336*x^77 + 324540216*x^75 + 3176716400*x^73 + 26088783435*x^71 + 182364632450*x^69 + 1096993404430*x^67 + 5727160371180*x^65 + 26123889412400*x^63 + 104656320045984*x^61 + 369731787035040*x^59 + 1155454041309504*x^57 + 3201570572795084*x^55 + 7877932561061640*x^53 + 17231414395464984*x^51 + 33516481089577200*x^49 + 57963796707857040*x^47 + 89067326568860640*x^45 + 121455445321173600*x^43 + 146721427591999680*x^41 + 156655690918541325*x^39 + 147405545359541742*x^37 + 121801604478231762*x^35 + 88004802264174740*x^33 + 55317304280338408*x^31 + 30067266499541040*x^29 + 14031391033119152*x^27 + 5574440580220512*x^25 + 1866442158555975*x^23 + 520341450264090*x^21 + 119032357903550*x^19 + 21945588357420*x^17 + 3188675231420*x^15 + 354860518600*x^13 + 29135916264*x^11 + 1677106640*x^9 + 62891499*x^7 + 1370754*x^5 + 14190*x^3 + 44*x
89:
x^88 + 87*x^86 + 3655*x^84 + 98770*x^82 + 1929501*x^80 + 29034396*x^78 + 350161812*x^76 + 3477216600*x^74 + 28987537150*x^72 + 205811513765*x^70 + 1258315963905*x^68 + 6681687099710*x^66 + 31022118677225*x^64 + 126600387152400*x^62 + 456002537343216*x^60 + 1454278362337824*x^58 + 4116305022165108*x^56 + 10358022441395860*x^54 + 23196134763125940*x^52 + 46252743903616536*x^50 + 82115378669464140*x^48 + 129728497393775280*x^46 + 182183167981760400*x^44 + 227068876035237600*x^42 + 250649105469666120*x^40 + 244382877832924467*x^38 + 209769429934732479*x^36 + 157890968768078210*x^34 + 103719945525634515*x^32 + 59132290782430712*x^30 + 29065024282889672*x^28 + 12220888964329584*x^26 + 4355031703297275*x^24 + 1300853625660225*x^22 + 321387366339585*x^20 + 64617565719070*x^18 + 10363194502115*x^16 + 1292706174900*x^14 + 121399651100*x^12 + 8217822536*x^10 + 377348994*x^8 + 10737573*x^6 + 163185*x^4 + 990*x^2 + 1
90:
x^89 + 88*x^87 + 3741*x^85 + 102340*x^83 + 2024785*x^81 + 30872016*x^79 + 377447148*x^77 + 3801756816*x^75 + 32164253550*x^73 + 231900297200*x^71 + 1440680596355*x^69 + 7778680504140*x^67 + 36749279048405*x^65 + 152724276564800*x^63 + 560658857389200*x^61 + 1824010149372864*x^59 + 5271759063474612*x^57 + 13559593014190944*x^55 + 31074067324187580*x^53 + 63484158299081520*x^51 + 115631859759041340*x^49 + 187692294101632320*x^47 + 271250494550621040*x^45 + 348524321356411200*x^43 + 397370533061665800*x^41 + 401038568751465792*x^39 + 357174975294274221*x^37 + 279692573246309972*x^35 + 191724747789809255*x^33 + 114449595062769120*x^31 + 59132290782430712*x^29 + 26252279997448736*x^27 + 9929472283517787*x^25 + 3167295784216200*x^23 + 841728816603675*x^21 + 183649923622620*x^19 + 32308782859535*x^17 + 4481381406320*x^15 + 476260169700*x^13 + 37353738800*x^11 + 2054455634*x^9 + 73629072*x^7 + 1533939*x^5 + 15180*x^3 + 45*x
91:
x^90 + 89*x^88 + 3828*x^86 + 105995*x^84 + 2123555*x^82 + 32801517*x^80 + 406481544*x^78 + 4151918628*x^76 + 35641470150*x^74 + 260887834350*x^72 + 1646492110120*x^70 + 9036996468045*x^68 + 43430966148115*x^66 + 183746395242025*x^64 + 687259244541600*x^62 + 2280012686716080*x^60 + 6726037425812436*x^58 + 17675898036356052*x^56 + 41432089765583440*x^54 + 86680293062207460*x^52 + 161884603662657876*x^50 + 269807672771096460*x^48 + 400978991944396320*x^46 + 530707489338171600*x^44 + 624439409096903400*x^42 + 651687674221131912*x^40 + 601557853127198688*x^38 + 489462003181042451*x^36 + 349615716557887465*x^34 + 218169540588403635*x^32 + 118264581564861424*x^30 + 55317304280338408*x^28 + 22150361247847371*x^26 + 7522327487513475*x^24 + 2142582442263900*x^22 + 505037289962205*x^20 + 96926348578605*x^18 + 14844575908435*x^16 + 1768966344600*x^14 + 158753389900*x^12 + 10272278170*x^10 + 450978066*x^8 + 12271512*x^6 + 178365*x^4 + 1035*x^2 + 1
92:
x^91 + 90*x^89 + 3916*x^87 + 109736*x^85 + 2225895*x^83 + 34826302*x^81 + 437353560*x^79 + 4529365776*x^77 + 39443226966*x^75 + 293052087900*x^73 + 1878392407320*x^71 + 10477677064400*x^69 + 51209646652255*x^67 + 220495674290430*x^65 + 839983521106400*x^63 + 2840671544105280*x^61 + 8550047575185300*x^59 + 22947657099830664*x^57 + 54991682779774384*x^55 + 117754360386395040*x^53 + 225368761961739396*x^51 + 385439532530137800*x^49 + 588671286046028640*x^47 + 801957983888792640*x^45 + 972963730453314600*x^43 + 1049058207282797712*x^41 + 1002596421878664480*x^39 + 846636978475316672*x^37 + 629308289804197437*x^35 + 409894288378212890*x^33 + 232714176627630544*x^31 + 114449595062769120*x^29 + 48402641245296107*x^27 + 17451799771031262*x^25 + 5309878226480100*x^23 + 1346766106565880*x^21 + 280576272201225*x^19 + 47153358767970*x^17 + 6250347750920*x^15 + 635013559600*x^13 + 47626016970*x^11 + 2505433700*x^9 + 85900584*x^7 + 1712304*x^5 + 16215*x^3 + 46*x
93:
x^92 + 91*x^90 + 4005*x^88 + 113564*x^86 + 2331890*x^84 + 36949857*x^82 + 470155077*x^80 + 4935847320*x^78 + 43595145594*x^76 + 328693558050*x^74 + 2139280241670*x^72 + 12124169174520*x^70 + 60246643120300*x^68 + 263926640438545*x^66 + 1023729916348425*x^64 + 3527930788646880*x^62 + 10830060261901380*x^60 + 29673694525643100*x^58 + 72667580816130436*x^56 + 159186450151978480*x^54 + 312049055023946856*x^52 + 547324136192795676*x^50 + 858478958817125100*x^48 + 1202936975833188960*x^46 + 1503671219791486200*x^44 + 1673497616379701112*x^42 + 1654284096099796392*x^40 + 1448194831602515360*x^38 + 1118770292985239888*x^36 + 759510004936100355*x^34 + 450883717216034179*x^32 + 232714176627630544*x^30 + 103719945525634515*x^28 + 39602161018878633*x^26 + 12832205713993575*x^24 + 3489348548829780*x^22 + 785613562163430*x^20 + 144079707346575*x^18 + 21094923659355*x^16 + 2403979904200*x^14 + 206379406870*x^12 + 12777711870*x^10 + 536878650*x^8 + 13983816*x^6 + 194580*x^4 + 1081*x^2 + 1
94:
x^93 + 92*x^91 + 4095*x^89 + 117480*x^87 + 2441626*x^85 + 39175752*x^83 + 504981379*x^81 + 5373200880*x^79 + 48124511370*x^77 + 368136785016*x^75 + 2432332329570*x^73 + 14002561581840*x^71 + 70724320184700*x^69 + 315136287090800*x^67 + 1244225590638855*x^65 + 4367914309753280*x^63 + 13670731806006660*x^61 + 38223742100828400*x^59 + 95615237915961100*x^57 + 214178132931752864*x^55 + 429803415410341896*x^53 + 772692898154535072*x^51 + 1243918491347262900*x^49 + 1791608261879217600*x^47 + 2305629203680278840*x^45 + 2646461346833015712*x^43 + 2703342303382594104*x^41 + 2450791253481179840*x^39 + 1965407271460556560*x^37 + 1388818294740297792*x^35 + 860778005594247069*x^33 + 465428353255261088*x^31 + 218169540588403635*x^29 + 88004802264174740*x^27 + 30284005485024837*x^25 + 8799226775309880*x^23 + 2132379668729310*x^21 + 424655979547800*x^19 + 68248282427325*x^17 + 8654327655120*x^15 + 841392966470*x^13 + 60403728840*x^11 + 3042312350*x^9 + 99884400*x^7 + 1906884*x^5 + 17296*x^3 + 47*x
95:
x^94 + 93*x^92 + 4186*x^90 + 121485*x^88 + 2555190*x^86 + 41507642*x^84 + 541931236*x^82 + 5843355957*x^80 + 53060358690*x^78 + 411731930610*x^76 + 2761025887620*x^74 + 16141841823510*x^72 + 82848489359220*x^70 + 375382930211100*x^68 + 1508152231077400*x^66 + 5391644226101705*x^64 + 17198662594653540*x^62 + 49053802362729780*x^60 + 125288932441604200*x^58 + 286845713747883300*x^56 + 588989865562320376*x^54 + 1084741953178481928*x^52 + 1791242627540058576*x^50 + 2650087220696342700*x^48 + 3508566179513467800*x^46 + 4150132566624501912*x^44 + 4376839919762295216*x^42 + 4105075349580976232*x^40 + 3413602103063071920*x^38 + 2507588587725537680*x^36 + 1620288010530347424*x^34 + 916312070471295267*x^32 + 450883717216034179*x^30 + 191724747789809255*x^28 + 69886166503903470*x^26 + 21631432489303455*x^24 + 5621728217559090*x^22 + 1210269541711230*x^20 + 212327989773900*x^18 + 29749251314475*x^16 + 3245372870670*x^14 + 266783135710*x^12 + 15820024220*x^10 + 636763050*x^8 + 15890700*x^6 + 211876*x^4 + 1128*x^2 + 1
96:
x^95 + 94*x^93 + 4278*x^91 + 125580*x^89 + 2672670*x^87 + 43949268*x^85 + 581106988*x^83 + 6348337336*x^81 + 58433559570*x^79 + 459856441980*x^77 + 3129162672636*x^75 + 18574174153080*x^73 + 96851050941060*x^71 + 446107250395800*x^69 + 1823288518168200*x^67 + 6635869816740560*x^65 + 21566576904406820*x^63 + 62724534168736440*x^61 + 163512674542432600*x^59 + 382460951663844400*x^57 + 803167998494073240*x^55 + 1514545368588823824*x^53 + 2563935525694593648*x^51 + 3894005712043605600*x^49 + 5300174441392685400*x^47 + 6455761770304780752*x^45 + 7023301266595310928*x^43 + 6808417652963570336*x^41 + 5864393356544251760*x^39 + 4472995859186094240*x^37 + 3009106305270645216*x^35 + 1777090076065542336*x^33 + 916312070471295267*x^31 + 409894288378212890*x^29 + 157890968768078210*x^27 + 51915437974328292*x^25 + 14420954992868970*x^23 + 3342649210440540*x^21 + 636983969321700*x^19 + 97997533741800*x^17 + 11899700525790*x^15 + 1108176102180*x^13 + 76223753060*x^11 + 3679075400*x^9 + 115775100*x^7 + 2118760*x^5 + 18424*x^3 + 48*x
97:
x^96 + 95*x^94 + 4371*x^92 + 129766*x^90 + 2794155*x^88 + 46504458*x^86 + 622614630*x^84 + 6890268572*x^82 + 64276915527*x^80 + 512916800670*x^78 + 3540894603246*x^76 + 21335200040700*x^74 + 112992892764570*x^72 + 528955739755020*x^70 + 2198671448379300*x^68 + 8144022047817960*x^66 + 26958221130508525*x^64 + 79923196763389980*x^62 + 212566476905162380*x^60 + 507749884105448600*x^58 + 1090013712241956540*x^56 + 2103535234151144200*x^54 + 3648677478873075576*x^52 + 5685248339583664176*x^50 + 7950261662089028100*x^48 + 9964327949818248552*x^46 + 11173433833219812840*x^44 + 11185257572725865552*x^42 + 9969468706125227992*x^40 + 7886597962249166160*x^38 + 5516694892996182896*x^36 + 3397378086595889760*x^34 + 1832624140942590534*x^32 + 860778005594247069*x^30 + 349615716557887465*x^28 + 121801604478231762*x^26 + 36052387482172425*x^24 + 8964377427999630*x^22 + 1847253511032930*x^20 + 310325523515700*x^18 + 41648951840265*x^16 + 4353548972850*x^14 + 343006888770*x^12 + 19499099620*x^10 + 752538150*x^8 + 18009460*x^6 + 230300*x^4 + 1176*x^2 + 1
98:
x^97 + 96*x^95 + 4465*x^93 + 134044*x^91 + 2919735*x^89 + 49177128*x^87 + 666563898*x^85 + 7471375560*x^83 + 70625252863*x^81 + 571350360240*x^79 + 4000751045226*x^77 + 24464362713336*x^75 + 131567066917650*x^73 + 625806790696080*x^71 + 2644778698775100*x^69 + 9967310565986160*x^67 + 33594090947249085*x^65 + 101489773667796800*x^63 + 275291011073898820*x^61 + 671262558647881200*x^59 + 1472474663905800940*x^57 + 2906703232645217440*x^55 + 5163222847461899400*x^53 + 8249183865278257824*x^51 + 11844267374132633700*x^49 + 15264502391210933952*x^47 + 17629195603524593592*x^45 + 18208558839321176480*x^43 + 16777886359088798328*x^41 + 13750991318793417920*x^39 + 9989690752182277136*x^37 + 6406484391866534976*x^35 + 3609714217008132870*x^33 + 1777090076065542336*x^31 + 759510004936100355*x^29 + 279692573246309972*x^27 + 87967825456500717*x^25 + 23385332420868600*x^23 + 5189902721473470*x^21 + 947309492837400*x^19 + 139646485582065*x^17 + 16253249498640*x^15 + 1451182990950*x^13 + 95722852680*x^11 + 4431613550*x^9 + 133784560*x^7 + 2349060*x^5 + 19600*x^3 + 49*x
99:
x^98 + 97*x^96 + 4560*x^94 + 138415*x^92 + 3049501*x^90 + 51971283*x^88 + 713068356*x^86 + 8093990190*x^84 + 77515521435*x^82 + 635627275767*x^80 + 4513667845896*x^78 + 28005257316582*x^76 + 152902266958350*x^74 + 738799683460650*x^72 + 3173734438530120*x^70 + 12165982014365460*x^68 + 41738112995067045*x^66 + 128447994798305325*x^64 + 355214207837288800*x^62 + 883829035553043580*x^60 + 1980224548011249540*x^58 + 3996716944887173980*x^56 + 7266758081613043600*x^54 + 11897861344151333400*x^52 + 17529515713716297876*x^50 + 23214764053299962052*x^48 + 27593523553342842144*x^46 + 29381992672540989320*x^44 + 27963143931814663880*x^42 + 23720460024918645912*x^40 + 17876288714431443296*x^38 + 11923179284862717872*x^36 + 7007092303604022630*x^34 + 3609714217008132870*x^32 + 1620288010530347424*x^30 + 629308289804197437*x^28 + 209769429934732479*x^26 + 59437719903041025*x^24 + 14154280149473100*x^22 + 2794563003870330*x^20 + 449972009097765*x^18 + 57902201338905*x^16 + 5804731963800*x^14 + 438729741450*x^12 + 23930713170*x^10 + 886322710*x^8 + 20358520*x^6 + 249900*x^4 + 1225*x^2 + 1
100:
x^99 + 98*x^97 + 4656*x^95 + 142880*x^93 + 3183545*x^91 + 54891018*x^89 + 762245484*x^87 + 8760554088*x^85 + 84986896995*x^83 + 706252528630*x^81 + 5085018206136*x^79 + 32006008361808*x^77 + 177366629671686*x^75 + 870366750378300*x^73 + 3799541229226200*x^71 + 14810760713140560*x^69 + 51705423561053205*x^67 + 162042085745554410*x^65 + 456703981505085600*x^63 + 1159120046626942400*x^61 + 2651487106659130740*x^59 + 5469191608792974920*x^57 + 10173461314258261040*x^55 + 17061084191613232800*x^53 + 25778699578994555700*x^51 + 35059031427432595752*x^49 + 42858025944553776096*x^47 + 47011188276065582912*x^45 + 46171702771135840360*x^43 + 40498346384007444240*x^41 + 31627280033224861216*x^39 + 21912870037044995008*x^37 + 13413576695470557606*x^35 + 7219428434016265740*x^33 + 3397378086595889760*x^31 + 1388818294740297792*x^29 + 489462003181042451*x^27 + 147405545359541742*x^25 + 37539612570341700*x^23 + 7984465725343800*x^21 + 1397281501935165*x^19 + 197548686920970*x^17 + 22057981462440*x^15 + 1889912732400*x^13 + 119653565850*x^11 + 5317936260*x^9 + 154143080*x^7 + 2598960*x^5 + 20825*x^3 + 50*x
Definition
The Fibonacci polynomials $F_n$ are defined by $F_0 = 0$, $F_1 = 1$ and $F_n(x) = x F_{n-1}(x) + F_{n-2}(x)$ for $n \geq 2$.
Parameters
$n$
—   integer ($n \geq 0$)
Formulas
(1)
$F_n(x) = \sum_{k=0}^{\lfloor (n-1)/2 \rfloor} \binom{n-k-1}{k} x^{n-2k-1}$.
(2)
$\sum_{n=0}^\infty F_n(x) t^n = \frac{t}{1 - xt - t^2}$.
(3)
$F_n(x) = \frac{\alpha^n - \beta^n}{\alpha - \beta}$, where $\alpha, \beta = \frac{x \pm \sqrt{x^2+4}}{2}$ are the roots of $z^2 - xz - 1$.
(4)
$L_n(x) = F_{n-1}(x) + F_{n+1}(x)$ and $F_{2n}(x) = F_n(x)L_n(x)$, where $L_n$ are the Lucas polynomials.
(5)
$L_n(x)^2 - (x^2+4)F_n(x)^2 = 4(-1)^n$.
(6)
$\gcd(F_m, F_n) = F_{\gcd(m,n)}$, so for $n > 2$ the polynomial $F_n$ divides $F_m$ exactly when $n$ divides $m$.
(7)
$F_n(x) = i^{n-1} U_{n-1}(-ix/2)$, where $U_n$ are the $U_n$.
Comments
(8)
At $x = 1$ the values are the Fibonacci numbers, and the ratio $F_{n+1}(1)/F_n(1)$ tends to the golden ratio, which is the larger root of $z^2 - z - 1$.
(9)
Some authors index these from $F_1 = 1$, so that every polynomial listed here appears one place earlier. The coefficients in [4] are indexed that way.
(10)
The same recurrence started at $2$ and $x$ gives the Lucas polynomials, which are listed separately.
(11)
For integers $P, Q$ the Lucas sequences [5] are the two solutions of $X_n = P X_{n-1} - Q X_{n-2}$ picked out by their starting values: $U_0 = 0$, $U_1 = 1$ and $V_0 = 2$, $V_1 = P$. The polynomials in this pair are the case $P = x$, $Q = -1$: $F_n(x) = U_n(x, -1)$ and $L_n(x) = V_n(x, -1)$.
(12)
[1] is a book-length treatment of both families and of the numbers they specialise to.
(13)
These are not orthogonal polynomials in the usual sense. A three-term recurrence $p_n = (x - c_n)p_{n-1} - k_n p_{n-2}$ gives a family orthogonal for a positive measure on $\mathbb{R}$ exactly when $k_n > 0$ (Favard), and here $k_n = -1$. What holds instead comes from $U_n$ through $F_n(x) = i^{n-1}U_{n-1}(-ix/2)$: along the segment $x = 2it$, $t \in [-1,1]$, with weight $\sqrt{1-t^2}$, distinct $F_m, F_n$ pair to zero, while $\langle F_n, F_n\rangle$ alternates between $\pm\pi/2$ — an indefinite form rather than an inner product.
Programs
(P1)
Sage
R. = ZZ[]
def fibonacci_polynomial(n):
    a, b = R(0), R(1)
    for _ in range(n):
        a, b = b, x*b + a
    return a

fibonacci_polynomial(101)        # the next one after this table
References
[1]
Koshy, T., "Fibonacci and Lucas Numbers with Applications", Wiley-Interscience, 2001.
Links
Data properties
Entries are of type: integral polynomial
Table is complete: no
How well the digits are known: exact


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