A274503 a(n) = 301*binomial(n-1,8)+52*binomial(n-1,7)+binomial(n-1,6).
0, 0, 1, 59, 745, 4665, 19995, 67287, 191103, 478335, 1085370, 2276560, 4476758, 8340982, 14844570, 25397490, 41986770, 67351314, 105193671, 160433625, 239508775, 350727575, 504680605, 714716145, 997486425, 1373571225, 1868185800, 2511980406, 3341939004
Offset: 5
Links
- Vincenzo Librandi, Table of n, a(n) for n = 5..1000
- Q. T. Bach, R. Paudyal, J. B. Remmel, A Fibonacci analogue of Stirling numbers, arXiv preprint arXiv:1510.04310 [math.CO], 2015 (page 25).
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Magma
[301*Binomial(n-1,8)+52*Binomial(n-1,7)+Binomial(n-1,6): n in [5..40]];
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Maple
A274503:=n->301*binomial(n-1,8)+52*binomial(n-1,7)+binomial(n-1,6): seq(A274503(n), n=5..50); # Wesley Ivan Hurt, Jun 25 2016
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Mathematica
Table[301*Binomial[n-1,8]+52*Binomial[n-1,7]+Binomial[n-1,6], {n, 5, 40}] -
PARI
concat([0, 0], Vec(x^7*(1 + 50*x + 250*x^2)/(1-x)^9 + O(x^100))) \\ Altug Alkan, Jun 26 2016
Formula
G.f.: x^7*(1 + 50*x + 250*x^2)/(1-x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
a(n) = (n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(301*n^2-4099*n+14000)/40320. - Wesley Ivan Hurt, Jun 25 2016