A355468 Expansion of Sum_{k>=0} (k^2 * x/(1 - k^2 * x))^k.

1, 1, 17, 858, 85988, 14318320, 3570592512, 1245401343760, 578840603221568, 345763649636940672, 258099498410703320960, 235426611021544158413824, 257654470061373320338925568, 333210260028337620911268462592

Offset: 0

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..211

Crossrefs

Cf. A195242, A242446, A249459.

Programs

PARI

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

PARI

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

Formula

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