A354413 - OEIS

%I #14 Jun 08 2022 09:59:04

%S 1,0,2,6,36,250,2100,20594,231168,2923722,41149140,637972522,

%T 10804678632,198480649250,3930963078588,83500876635570,

%U 1893745346613216,45672635292831322,1167233799092342148,31510575263852229242,896028017040096045720

%N Expansion of e.g.f. 1/(2 - exp(x))^x.

%F a(0) = 1; a(n) = Sum_{k=1..n} A052862(k) * binomial(n-1,k-1) * a(n-k).

%F a(n) ~ n! / (Gamma(log(2)) * 2^log(2) * n^(1 - log(2)) * log(2)^(n + log(2))). - _Vaclav Kotesovec_, Jun 08 2022

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x))^x))

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, (k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A000629, A000670, A052862, A351739, A354412.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 25 2022