A360832 Expansion of Sum_{k>=0} ( k * x / (1 - (k * x)^2) )^k.

1, 1, 4, 28, 288, 3855, 63232, 1227291, 27511296, 699389444, 19880700928, 624817997477, 21512488648704, 805233062024021, 32556682898653184, 1413981749074790444, 65652661019642560512, 3245240681196968168619, 170146759140135777861632

Offset: 0

Author

Seiichi Manyama, Feb 22 2023

Keywords

• nonn

Crossrefs

Cf. A195242, A360833.

Cf. A338661, A360810, A360834.

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\2, (n-2*k)^n*binomial(n-k-1, k));

Formula

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