A355472 Expansion of Sum_{k>=0} (x/(1 - k^3 * x))^k.

1, 1, 2, 18, 275, 6680, 258897, 13646776, 959706169, 88651586048, 10272048320897, 1462972094910224, 253355867842243905, 52387780870782231424, 12745274175326359046785, 3615579524073585972982544, 1184928928181459098548941633, 444427677344332049739011858432

Offset: 0

Author

Seiichi Manyama, Jul 03 2022

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..235

Crossrefs

Cf. A080108, A355463, A355471.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^3*x))^k))

PARI

a(n) = if(n==0, 1, sum(k=1, n, k^(3*(n-k))*binomial(n-1, k-1)));

Formula

a(n) = Sum_{k=1..n} k^(3*(n-k)) * binomial(n-1,k-1) for n > 0.