A356577 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^x.

1, 0, 2, 6, 28, 195, 1248, 11200, 97088, 1036602, 11477230, 142038996, 1883459928, 27044341896, 412487825540, 6745633845210, 116679466051968, 2137078798914128, 41252266236703320, 838320793571448408, 17846205347898263960, 398262850748807921856

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k * A308345(k-1) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k)^x))
(PARI) a308345(n) = n!*sumdiv(n, d, 1/(d*(n/d)^d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a308345(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A308345, A356408.

Sequence in context: A372349 A111342 A008964 * A058128 A229112 A201959

Adjacent sequences: A356574 A356575 A356576 * A356578 A356579 A356580

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2022

Status

approved