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

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

Prog

(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;

Crossrefs

Cf. A000041, A006950, A356530, A356540.

Cf. A090879.

Sequence in context: A105631 A167019 A376587 * A342904 A230563 A204266

Adjacent sequences: A356535 A356536 A356537 * A356539 A356540 A356541

Keyword

nonn

Author

Seiichi Manyama, Aug 11 2022

Status

approved