A356598 Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^exp(x).

1, 1, 8, 60, 606, 6795, 96145, 1458051, 25584020, 487911129, 10231475323, 230541036627, 5647620829862, 146760059424017, 4075332758190265, 119876230004510557, 3727336891407329320, 121841674696261466385, 4187995620589733257695, 150589951713517027739551

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354340(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-k*x^k)^exp(x)))
(PARI) a354340(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d+1))/(k*(n-k)!));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354340(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A353993, A354340.

Sequence in context: A317774 A099337 A356595 * A075147 A034664 A242084

Adjacent sequences: A356595 A356596 A356597 * A356599 A356600 A356601

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2022

Status

approved