A356599 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^exp(x).

1, 1, 5, 25, 159, 1201, 10488, 102901, 1121375, 13406353, 174284898, 2445111373, 36799134584, 591042564425, 10086822013726, 182218681622851, 3472980343846199, 69632877583186121, 1464890891351327598, 32260213678562913097, 742152913359395190170

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354341(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/k!)^exp(x)))
(PARI) a354341(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!^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, a354341(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A354341, A356409.

Sequence in context: A179324 A097145 A085644 * A137963 A366435 A144887

Adjacent sequences: A356596 A356597 A356598 * A356600 A356601 A356602

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2022

Status

approved