A356595 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^k )^exp(x).
1, 1, 8, 60, 582, 6555, 88585, 1333731, 22602020, 420261225, 8536210843, 187294058787, 4420961159582, 111409233290537, 2986570482052729, 84773698697674837, 2539347801355477960, 80003306259203052465, 2644032803825175398175, 91425359712959262036223
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^k)^exp(x))) -
PARI
a356600(n) = n!*sum(k=1, n, sigma(k, 2)/(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, a356600(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A356600(k) * binomial(n-1,k-1) * a(n-k).