A356542 Expansion of e.g.f. Product_{k>0} 1/(1 - k! * x^k)^(1/k!).

1, 1, 4, 18, 132, 900, 11160, 100800, 1809360, 25053840, 608428800, 8610386400, 469291838400, 7110609105600, 404607162960000, 13958116204032000, 821937470818464000, 17420311428103584000, 2860701872247483264000, 60029296274562398784000

Offset: 0

Author

Seiichi Manyama, Aug 11 2022

Keywords

• nonn

Crossrefs

Cf. A209902, A356524, A356541.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k!*x^k)^(1/k!))))

PARI

a356541(n) = sumdiv(n, d, d*d!^(n/d-1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a356541(j)*v[i-j+1]/(i-j)!)); v;

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A356541(k) * a(n-k)/(n-k)!.