A356575 Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^x.

1, 0, 2, 6, 24, 185, 990, 9877, 72968, 824553, 8495560, 102689741, 1317098772, 18729163609, 270642677396, 4396374315075, 73997950572016, 1318896555293137, 24900891903482832, 499312682762581945, 10301544926241347140, 227464062944112566481

Offset: 0

Author

Seiichi Manyama, Aug 12 2022

Keywords

• nonn

Crossrefs

Cf. A087906, A356025, A356576.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k!))^x))

PARI

a087906(n) = (n-1)!*sumdiv(n, d, 1/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a087906(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k * A087906(k-1) * binomial(n-1,k-1) * a(n-k).