A356596 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^(1/k!) )^exp(x).
1, 1, 5, 25, 162, 1231, 10988, 109481, 1220005, 14915924, 198841997, 2861122716, 44290863499, 731732469209, 12865489418525, 239613961313353, 4712991199268122, 97557259778360215, 2120682504988009054, 48270952330701285107, 1148400573894718809487
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k!))^exp(x))) -
PARI
a354338(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!))/(n-k)!); a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354338(j)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A354338(k) * binomial(n-1,k-1) * a(n-k).