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A356599
Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^exp(x).
0
1, 1, 5, 25, 159, 1201, 10488, 102901, 1121375, 13406353, 174284898, 2445111373, 36799134584, 591042564425, 10086822013726, 182218681622851, 3472980343846199, 69632877583186121, 1464890891351327598, 32260213678562913097, 742152913359395190170
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A354341(k) * 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!)^exp(x)))
(PARI) a354341(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!^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, a354341(j)*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
Sequence in context: A179324 A097145 A085644 * A137963 A366435 A144887
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved