A360818 Expansion of Sum_{k>=0} ( (k*x)^2 / (1 - k*x) )^k.

1, 0, 1, 1, 17, 65, 922, 7074, 106183, 1248479, 21144289, 331763177, 6441011484, 124904347404, 2773880604749, 63538143151589, 1600211849569585, 42076439530000297, 1189408501356380558, 35214128238218917974, 1106088535644470694779

Offset: 0

Author

Seiichi Manyama, Feb 21 2023

Keywords

• nonn

Crossrefs

Cf. A195242, A360819.

Cf. A360708.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, ((k*x)^2/(1-k*x))^k))

PARI

a(n) = sum(k=0, n\2, k^n*binomial(n-k-1, n-2*k));

Formula

a(n) = Sum_{k=0..floor(n/2)} k^n * binomial(n-k-1,n-2*k).