A349856 Expansion of Sum_{k>=0} x^k/(1 + k^2 * x).

1, 1, 0, -2, 7, 3, -242, 2032, -3795, -187211, 3860140, -36467310, -284357501, 21796446487, -538332144294, 5605176351652, 182065102478857, -12963817679287959, 422751776737348504, -5483284328996107802, -327213964461103956801, 30082452646697648945899

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..343

Formula

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

Mathematica

a[n_] := Sum[If[k == n - k == 0, 1, (-k^2)^(n - k)], {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, Dec 03 2021 *)

Prog

(PARI) a(n, s=0, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^2*x)))

Crossrefs

Cf. A349857, A349858, A349889.

Sequence in context: A249782 A090564 A306618 * A079072 A004584 A016592

Adjacent sequences: A349853 A349854 A349855 * A349857 A349858 A349859

Keyword

sign

Author

Seiichi Manyama, Dec 02 2021

Status

approved