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 A351155 #16 May 04 2022 04:53:03
%S A351155 1,0,0,3,0,15,90,210,2520,13230,103950,873180,7484400,72972900,
%T A351155 745404660,8185126950,95805309600,1184852869200,15538995271800,
%U A351155 214159261516200,3109622647131000,47252530639314000,752635500963746400,12499951421009052000,216709136059079664000
%N A351155 Expansion of e.g.f. (1 - x^2/2)^(-x).
%F A351155 a(0) = 1; a(n) = (n-1)! * Sum_{k=2..floor((n+1)/2)} (2*k-1)/((k-1) * 2^(k-1)) * a(n-2*k+1)/(n-2*k+1)!.
%F A351155 a(n) = n! * Sum_{k=0..floor(n/2)} |Stirling1(k,n-2*k)|/(2^k*k!).
%F A351155 a(n) ~ sqrt(Pi) * n^(n - 1/2 + sqrt(2)) / (Gamma(sqrt(2)) * exp(n) * 2^(n/2 + sqrt(2) - 1/2)). - _Vaclav Kotesovec_, May 04 2022
%o A351155 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2/2)^(-x)))
%o A351155 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*log(1-x^2/2))))
%o A351155 (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+1)\2, (2*j-1)/((j-1)*2^(j-1))*v[i-2*j+2]/(i-2*j+1)!)); v;
%o A351155 (PARI) a(n) = n!*sum(k=0, n\2, abs(stirling(k, n-2*k, 1))/(2^k*k!));
%Y A351155 Cf. A351156, A353226.
%K A351155 nonn
%O A351155 0,4
%A A351155 _Seiichi Manyama_, May 02 2022