A274501 a(n) = 25*binomial(n-1,6) + binomial(n-1,5).
0, 1, 31, 196, 756, 2226, 5502, 12012, 23892, 44187, 77077, 128128, 204568, 315588, 472668, 689928, 984504, 1376949, 1891659, 2557324, 3407404, 4480630, 5821530, 7480980, 9516780, 11994255, 14986881, 18576936, 22856176, 27926536, 33900856, 40903632, 49071792
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 (7,-21,35,-35,21,-7,1).
Crossrefs
Cf. A253945.
Programs
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Magma
[25*Binomial(n-1,6)+Binomial(n-1,5): n in [5..40]];
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Maple
A274501:=n->25*binomial(n-1,6) + binomial(n-1,5): seq(A274501(n), n=5..50); # Wesley Ivan Hurt, Jun 25 2016
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Mathematica
Table[25 Binomial[n - 1, 6] + Binomial[n - 1, 5], {n, 5, 40}] LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,31,196,756,2226,5502},40] (* Harvey P. Dale, Mar 09 2022 *) -
PARI
concat(0, Vec(x^6*(1+24*x)/(1-x)^7 + O(x^99))) \\ Altug Alkan, Jun 27 2016
Formula
G.f.: x^6*(1 + 24*x)/(1-x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
a(n) = (n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(25*n-144)/720. - Wesley Ivan Hurt, Jun 25 2016