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

0,3

Links

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

Formula

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

Prog

(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)));

Crossrefs

Cf. A080108, A355463, A355471.

Sequence in context: A334242 A349314 A365555 * A295183 A351768 A294193

Adjacent sequences: A355469 A355470 A355471 * A355473 A355474 A355475

Keyword

nonn

Author

Seiichi Manyama, Jul 03 2022

Status

approved