A349859 Expansion of Sum_{k>=0} k * x^k/(1 + k^2 * x).

0, 1, 1, -4, 8, 57, -771, 4168, 22504, -943255, 13349105, -48905364, -3284972544, 117005181841, -2071095992867, -2153841382168, 1791029813641424, -79511121545541327, 1867021096818903489, 8850156160819959100, -3592582141732300745000

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Crossrefs

Cf. A349860, A349861.

Programs

Mathematica

a[n_] := Sum[If[k == n - k == 0, 1, (-k^2)^(n-k)] * k, {k, 0, n}]; Array[a, 21, 0] (* Amiram Eldar, Dec 03 2021 *)

PARI

a(n, s=1, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);

PARI

my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k*x^k/(1+k^2*x))))

Formula

a(n) = Sum_{k=0..n} (-k^2)^(n-k) * k.