A360730 Expansion of Sum_{k>=0} (k * x * (1 + k*x^2))^k.

1, 1, 4, 28, 272, 3368, 50768, 902397, 18481408, 428556075, 11099001600, 317544062217, 9946366838784, 338537433281448, 12441407233436672, 491002325860132371, 20710640842719301632, 929821866165431838038, 44270378887441746923520

Offset: 0

Author

Seiichi Manyama, Feb 18 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A360618, A360731.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\3, (n-2*k)^(n-k)*binomial(n-2*k, k));

Formula

a(n) = Sum_{k=0..floor(n/3)} (n-2*k)^(n-k) * binomial(n-2*k,k).