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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 25 2016
STATUS
approved