A356596 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^(1/k!) )^exp(x).

1, 1, 5, 25, 162, 1231, 10988, 109481, 1220005, 14915924, 198841997, 2861122716, 44290863499, 731732469209, 12865489418525, 239613961313353, 4712991199268122, 97557259778360215, 2120682504988009054, 48270952330701285107, 1148400573894718809487

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354338(k) * 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)^(1/k!))^exp(x)))
(PARI) a354338(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!))/(n-k)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354338(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A354338, A356025.

Sequence in context: A144887 A181344 A361916 * A134007 A125794 A109793

Adjacent sequences: A356593 A356594 A356595 * A356597 A356598 A356599

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2022

Status

approved