A356590 Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^exp(x).

1, 1, 8, 96, 2382, 100035, 6995185, 699004551, 96910745876, 17476222963065, 4000562831147323, 1127335505294104887, 384099492016873956422, 155403154609857016567601, 73680868272553092728379865, 40444727351284600806487687057

Offset: 0

Author

Seiichi Manyama, Aug 14 2022

Keywords

• nonn

Crossrefs

Cf. A346545, A346547.

Cf. A023881, A356588, A356589.

Programs

PARI

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

PARI

a356589(n) = n!*sum(k=1, n, sigma(k, k)/(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, a356589(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356589(k) * binomial(n-1,k-1) * a(n-k).