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 A354309 #21 Jan 10 2025 15:00:46
%S A354309 1,0,2,6,44,360,3744,46200,662864,10838016,198943200,4050937440,
%T A354309 90613710912,2208677328000,58265734055424,1653914478303360,
%U A354309 50263564166365440,1628300694034022400,56012708047907510784,2039053421375533094400,78314004507947110456320
%N A354309 Expansion of e.g.f. 1/(1 - 2*x)^(x/2).
%F A354309 a(0) = 1; a(n) = (n-1)! * Sum_{k=2..n} k * 2^(k-2)/(k-1) * a(n-k)/(n-k)!.
%F A354309 a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-2*k) * |Stirling1(n-k,k)|/(n-k)!.
%F A354309 a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 1/4) / (Gamma(1/4) * exp(n)). - _Vaclav Kotesovec_, Mar 14 2024
%t A354309 With[{nn=20},CoefficientList[Series[1/(1-2x)^(x/2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 10 2025 *)
%o A354309 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x)^(x/2)))
%o A354309 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*2^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
%o A354309 (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A354309 Cf. A066166, A354310.
%Y A354309 Cf. A053491, A354311, A354315, A354319.
%K A354309 nonn
%O A354309 0,3
%A A354309 _Seiichi Manyama_, May 23 2022