This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354413 #16 Apr 03 2025 10:50:20 %S A354413 1,0,2,6,36,250,2100,20594,231168,2923722,41149140,637972522, %T A354413 10804678632,198480649250,3930963078588,83500876635570, %U A354413 1893745346613216,45672635292831322,1167233799092342148,31510575263852229242,896028017040096045720 %N A354413 Expansion of e.g.f. 1/(2 - exp(x))^x. %F A354413 a(0) = 1; a(n) = Sum_{k=1..n} A052862(k) * binomial(n-1,k-1) * a(n-k). %F A354413 a(n) ~ n! / (Gamma(log(2)) * 2^log(2) * n^(1 - log(2)) * log(2)^(n + log(2))). - _Vaclav Kotesovec_, Jun 08 2022 %t A354413 With[{nn=20},CoefficientList[Series[1/(2-Exp[x])^x,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 03 2025 *) %o A354413 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x))^x)) %o A354413 (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 A354413 Cf. A000629, A000670, A052862, A351739, A354412. %K A354413 nonn %O A354413 0,3 %A A354413 _Seiichi Manyama_, May 25 2022