A355495 Expansion of Sum_{k>=0} (k^2 * x/(1 - x))^k.

1, 1, 17, 762, 67772, 10032208, 2226273192, 691431572992, 286268594755712, 152365547943819264, 101361042063083269520, 82409537565402784477984, 80397802305461995791664944, 92692687015689239272783171264

Offset: 0

Author

Seiichi Manyama, Jul 04 2022

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..213

Crossrefs

Cf. A355494, A355496.

Cf. A323280.

Programs

PARI

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

PARI

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

Formula

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