A274502 a(n) = 90*binomial(n-1,7) + 9*binomial(n-1,6).
0, 0, 9, 153, 972, 3996, 12690, 33858, 79596, 169884, 335907, 624195, 1101672, 1861704, 3031236, 4779108, 7325640, 10953576, 16020477, 22972653, 32360724, 44856900, 61274070, 82586790, 109954260, 144745380, 188565975, 243288279, 311082768, 394452432
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 (8,-28,56,-70,56,-28,8,-1).
Crossrefs
Cf. A274501.
Programs
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Magma
[90*Binomial(n-1,7) + 9*Binomial(n-1,6): n in [5..40]];
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Maple
A274502:=n->90*binomial(n-1,7) + 9*binomial(n-1,6): seq(A274502(n), n=5..50); # Wesley Ivan Hurt, Jun 25 2016
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Mathematica
Table[90 Binomial[n-1, 7] + 9 Binomial[n-1, 6], {n, 5, 40}] LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,0,9,153,972,3996,12690,33858},30] (* Harvey P. Dale, Nov 01 2019 *) -
PARI
concat([0, 0], Vec(x^7*(9 + 81*x)/(1-x)^8 + O(x^100))) \\ Altug Alkan, Jun 26 2016
Formula
G.f.: x^7*(9 + 81*x)/(1-x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>11.
a(n) = (n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(10*n-63)/560. - Wesley Ivan Hurt, Jun 25 2016