A355718 - OEIS

%I #12 Jul 15 2022 15:04:28

%S 1,1,3,16,117,1071,11725,149122,2158401,35006941,628552231,

%T 12372376116,264849067549,6124239060915,152099146415385,

%U 4037206919213686,114038575520545153,3415098936831144537,108065651366801837611,3602585901321224507992

%N Expansion of e.g.f. exp( x/(1 + log(1-x)) ).

%F a(0) = 1; a(n) = Sum_{k=1..n} A052860(k) * binomial(n-1,k-1) * a(n-k).

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

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

%o (PARI) a007840(n) = sum(k=0, n, k!*abs(stirling(n, k, 1)));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*a007840(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A355719, A355720.

%Y Cf. A007840, A052860.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 15 2022