A360814 Expansion of Sum_{k>=0} x^(2*k) / (1 - k*x)^(k+1).

1, 0, 1, 2, 4, 10, 30, 98, 338, 1240, 4877, 20496, 91213, 426678, 2090081, 10702438, 57193760, 318283388, 1840036058, 11026424446, 68370955450, 438039068726, 2896018310881, 19733372875632, 138418266287689, 998363508783924, 7396739279819185, 56239695790595786

Offset: 0

Author

Seiichi Manyama, Feb 21 2023

Keywords

• nonn

Crossrefs

Cf. A360708.

Programs

PARI

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

PARI

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

Formula

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