A356440 Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^(1/(1-x)).

1, 1, 8, 99, 2444, 101450, 7045194, 701736966, 97147459184, 17505366041880, 4005462950166600, 1128394974054308400, 384386423684496873672, 155497732356686080354968, 73718160600338917089657216, 40462026280443230503858113240

Offset: 0

Author

Seiichi Manyama, Aug 07 2022

Keywords

• nonn

Crossrefs

Cf. A356437, A356439.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(k*x)^k)^(1/k))^(1/(1-x))))

PARI

a356437(n) = n!*sum(k=1, n, sigma(k, k)/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356437(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356437(k) * binomial(n-1,k-1) * a(n-k).