A349861 Expansion of Sum_{k>=0} k * x^k/(1 + k^4 * x).

0, 1, 1, -28, 272, 10473, -1204227, 61879504, 5542428184, -2801375692615, 597270865802225, -6353098642040604, -85053828910331125224, 62048537484671306803057, -23357096658814809538526243, -10072546328972154349642665952

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Crossrefs

Cf. A349859, A349860.

Programs

Mathematica

a[n_] := Sum[If[k == n - k == 0, 1, (-k^4)^(n-k)] * k, {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Dec 03 2021 *)

PARI

a(n, s=1, t=4) = sum(k=0, n, (-k^t)^(n-k)*k^s);

PARI

my(N=20, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k*x^k/(1+k^4*x))))

Formula

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