A360834 Expansion of Sum_{k>=0} (k * x)^k / (1 - (k * x)^2)^(k+1).

1, 1, 4, 29, 304, 4100, 67520, 1314167, 29520128, 751658635, 21393444864, 673046604600, 23192501108736, 868730852002205, 35145114836811776, 1527192185786650417, 70941146068492943360, 3508043437942077557884, 183989995827118805352448

Offset: 0

Author

Seiichi Manyama, Feb 22 2023

Keywords

• nonn

Crossrefs

Cf. A072034, A360835.

Cf. A000045, A360782, A360787.

Programs

PARI

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

PARI

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

Formula

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