A356597 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^exp(x).

1, 1, 5, 26, 172, 1354, 12403, 127945, 1471006, 18589503, 255951308, 3808299648, 60871219649, 1039240205691, 18868377309780, 362838034712928, 7364831540699076, 157305165900364641, 3526069495916583260, 82744901973286823822, 2028396974232995349291

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354339(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) a354339(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, a354339(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A354339, A356408.

Sequence in context: A057793 A090226 A355672 * A094422 A346545 A179513

Adjacent sequences: A356594 A356595 A356596 * A356598 A356599 A356600

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2022

Status

approved