%I #9 Aug 13 2022 11:28:42

%S 1,0,2,6,24,170,990,8267,67928,661698,6923010,78997457,983728812,

%T 13101433501,187893745130,2869108871085,46643882262448,

%U 803224515183482,14618310020427402,280340253237270977,5651276469430635620,119483759770082806035,2644015844432596590946

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

%F a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k * A182926(k-1) * binomial(n-1,k-1) * a(n-k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k!)^x))

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

%o 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;

%Y Cf. A182926, A356409.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 12 2022