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 A354412 #14 Feb 12 2024 18:49:25
%S A354412 1,0,1,3,15,95,735,6727,71169,854919,11497845,171179261,2795081751,
%T A354412 49668211177,954226247247,19709181213555,435524370171393,
%U A354412 10252531220906051,256148413939459917,6769302493147288885,188664988853982963735,5530544750788380455433
%N A354412 Expansion of e.g.f. 1/(2 - exp(x))^(x/2).
%F A354412 a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A052862(k) * binomial(n-1,k-1) * a(n-k).
%F A354412 a(n) ~ n! / (Gamma(log(2)/2) * 2^(log(2)/2) * n^(1 - log(2)/2) * log(2)^(n + log(2)/2)). - _Vaclav Kotesovec_, Jun 08 2022
%t A354412 With[{nn=30},CoefficientList[Series[1/(2-Exp[x])^(x/2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 12 2024 *)
%o A354412 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x))^(x/2)))
%o A354412 (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])/2); v;
%Y A354412 Cf. A000670, A052862, A354239, A354413.
%K A354412 nonn
%O A354412 0,4
%A A354412 _Seiichi Manyama_, May 25 2022