A356538 Expansion of e.g.f. Product_{k>0} 1/(1 - (2 * x)^k)^(1/2^k).

1, 1, 5, 27, 249, 2085, 30645, 354375, 6542865, 108554985, 2330525925, 45331607475, 1288779532425, 28889867731725, 876160258298325, 25315531795929375, 860642393272286625, 26527678331237708625, 1063065483349950205125, 36393649136002135852875

Offset: 0

Author

Seiichi Manyama, Aug 11 2022

Keywords

• nonn

Crossrefs

Cf. A000041, A006950, A356530, A356540.

Cf. A090879.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(2*x)^k)^(1/2^k))))

PARI

a090879(n) = sumdiv(n, d, d*2^(n-d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a090879(j)*v[i-j+1]/(i-j)!)); v;

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A090879(k) * a(n-k)/(n-k)!.