A349858 Expansion of Sum_{k>=0} x^k/(1 + k^4 * x).

1, 1, 0, -14, 175, 2211, -400994, 25610260, 582496701, -666933657755, 166042332973276, -14222991979095594, -14297382182023795925, 12622343477815735821511, -5840589387156997753180230, -443718496524920696265166664, 5189349322544398120691167482361

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..196

Crossrefs

Cf. A349856, A349857.

Programs

Mathematica

a[n_] := Sum[If[k == n - k == 0, 1, (-k^4)^(n-k)], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Dec 03 2021 *)

PARI

a(n, s=0, t=4) = 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^4*x)))

Formula

a(n) = Sum_{k=0..n} (-k^4)^(n-k).