A356554 - OEIS

%I #19 Aug 13 2022 11:27:50

%S 1,0,2,15,92,930,8514,116760,1445744,23020200,373858920,6756785640,

%T 130982295432,2751191997840,61046788571664,1445520760702200,

%U 36387213668348160,960383111961228480,26780931923301572544,781864626481646405760,23925584882896903854720

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

%F 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).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^k)^x))

%o (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;

%Y Cf. A354623, A355064.

%Y Cf. A001157, A066166, A356337, A356566.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 12 2022