A352983 a(n) = Sum_{k=0..floor(n/2)} k^(2*n).

1, 0, 1, 1, 257, 1025, 535538, 4799354, 4338079554, 69107159370, 96470431101379, 2401809362313955, 4798267740520031875, 172076350440523281571, 466164803742660494432996, 22761346686115003736962100, 80340572151131167125889902852

Offset: 0

Author

Seiichi Manyama, Apr 13 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..240

Crossrefs

Cf. A249459, A352984.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[k^(2*n), {k, 0, Floor[n/2]}]; Array[a, 17, 0] (* Amiram Eldar, Apr 13 2022 *)

PARI

a(n) = sum(k=0, n\2, k^(2*n));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x)^(2*k)/(1-k^2*x)))

Formula

G.f.: Sum_{k>=0} (k^2 * x)^(2 * k) / (1 - k^2 * x).

a(n) ~ exp(3 + (-1)^n) * (n/2)^(2*n) / (exp(4) - 1). - Vaclav Kotesovec, Apr 14 2022