A349857 Expansion of Sum_{k>=0} x^k/(1 + k^3 * x).

1, 1, 0, -6, 37, 155, -11616, 251940, 783641, -454238419, 29895012768, -757531311386, -106105977022243, 21452688824818775, -2105573104903303616, 16702280440994303008, 48278492787774402969521, -13301912828187822051695559, 1964564462643243537548661568

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..247

Crossrefs

Cf. A349856, A349858, A349902.

Programs

Mathematica

a[n_] := Sum[If[k == n - k == 0, 1, (-k^3)^(n-k)], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 03 2021 *)

PARI

a(n, s=0, t=3) = sum(k=0, n, (-k^t)^(n-k)*k^s);

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^3*x)))

Formula

a(n) = Sum_{k=0..n} (-k^3)^(n-k).