A316088 Expansion of 1/(1 + Sum_{k>=1} k^3 * x^k).

1, -1, -7, -12, 31, 193, 240, -1105, -5167, -3924, 36343, 133873, 31584, -1131025, -3343639, 1240212, 33732367, 79895089, -90574128, -970716385, -1800454975, 3954181452, 27045519079, 37164094177, -145299908928, -730358292769, -653629025575, 4869632030004

Offset: 0

Author

Seiichi Manyama, Jun 24 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..2000

Crossrefs

1/(1+ Sum_{k>=1} k^m * x^k): A163810 (m=1), A316087 (m=2), this sequence (m=3).

Programs

PARI

N=99; x='x+O('x^N); Vec((x-1)^4/(x^4-3*x^3+10*x^2-3*x+1))

Formula

G.f.: (x-1)^4/(x^4-3*x^3+10*x^2-3*x+1).

a(0) = 1; a(n) = -Sum_{k=1..n} k^3 * a(n-k). - Ilya Gutkovskiy, Feb 02 2021