A356554 Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^k )^x.

1, 0, 2, 15, 92, 930, 8514, 116760, 1445744, 23020200, 373858920, 6756785640, 130982295432, 2751191997840, 61046788571664, 1445520760702200, 36387213668348160, 960383111961228480, 26780931923301572544, 781864626481646405760, 23925584882896903854720

Offset

0,3

Links

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

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * sigma_2(k-1)/(k-1) * 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)^x))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*sigma(j-1, 2)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A354623, A355064.

Cf. A001157, A066166, A356337, A356566.

Sequence in context: A037641 A361303 A288952 * A356578 A362768 A258390

Adjacent sequences: A356551 A356552 A356553 * A356555 A356556 A356557

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2022

Status

approved