A349963 a(n) = Sum_{k=0..n} (2*k)^n.

1, 2, 20, 288, 5664, 141600, 4298944, 153638912, 6319260672, 294044152320, 15272286131200, 875880428003328, 54976337351106560, 3748609104907476992, 275924407293425336320, 21806398621389422592000, 1841661678145084557099008, 165530736067119754944577536

Offset: 0

Author

Seiichi Manyama, Dec 07 2021

Keywords

• nonn

Crossrefs

Cf. A031971, A185393, A249459, A349970.

Programs

Mathematica

a[n_] := Sum[If[k == n == 0, 1, (2*k)^n], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Dec 07 2021 *)

PARI

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

PARI

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

Formula

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

a(n) = 2^n * A031971(n).

a(n) ~ c * 2^n * n^n, where c = 1/(1 - 1/exp(1)) = A185393. - Vaclav Kotesovec, Dec 07 2021