A356579 - OEIS

A356579

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

1, 0, 2, 6, 24, 170, 990, 8267, 67928, 661698, 6923010, 78997457, 983728812, 13101433501, 187893745130, 2869108871085, 46643882262448, 803224515183482, 14618310020427402, 280340253237270977, 5651276469430635620, 119483759770082806035, 2644015844432596590946

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k * A182926(k-1) * 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!)^x))

(PARI) a182926(n) = n!*sumdiv(n, d, 1/(d*(n/d)!^d));

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a182926(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

CROSSREFS