A356461 - OEIS

A356461

Expansion of e.g.f. ( Product_{k>0} B(x^k)^k )^(1/(1-x)) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.

1, 1, 8, 62, 631, 7417, 104489, 1648845, 29319588, 572982162, 12250559615, 283321630605, 7053444523393, 187711377451249, 5317981377046420, 159652557864884330, 5061465465801168419, 168886786171198864725, 5914650120884760212977, 216844308186908733542877

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} A356459(k) * binomial(n-1,k-1) * a(n-k).

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(x^k)-1)^k)^(1/(1-x))))

(PARI) a356459(n) = n!*sum(k=1, n, sumdiv(k, d, d/(k/d)!));

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356459(j)*binomial(i-1, j-1)*v[i-j+1])); v;

CROSSREFS