A355720 - OEIS

%I #17 Jul 15 2022 15:05:02

%S 1,1,3,16,113,986,10237,123096,1680737,25668766,433329461,8009178596,

%T 160802065393,3483842906610,80992799730221,2010720004254856,

%U 53081510001375041,1484613248976841958,43846812123456425221,1363477059263944382604

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

%F a(0) = 1; a(n) = Sum_{k=1..n} A052882(k) * binomial(n-1,k-1) * a(n-k).

%F a(n) ~ n^(n - 1/4) * exp(sqrt(2*n) - 1/4 - n) / (sqrt(2) * log(2)^n). - _Vaclav Kotesovec_, Jul 15 2022

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(2-exp(x)))))

%o (PARI) a000670(n) = sum(k=0, n, k!*stirling(n, k, 2));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*a000670(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A000248, A355718, A355719.

%Y Cf. A000670, A052882, A075729.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 15 2022