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

5,3

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).

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

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

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 *)

Prog

(Magma) [90*Binomial(n-1, 7) + 9*Binomial(n-1, 6): n in [5..40]];
(PARI) concat([0, 0], Vec(x^7*(9 + 81*x)/(1-x)^8 + O(x^100))) \\ Altug Alkan, Jun 26 2016

Crossrefs

Cf. A274501.

Sequence in context: A089916 A143000 A143905 * A249642 A093849 A165232

Adjacent sequences: A274499 A274500 A274501 * A274503 A274504 A274505

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 25 2016

Status

approved