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 A354395 #11 May 25 2022 09:15:38
%S A354395 1,0,-1,-3,-4,15,149,672,1091,-12855,-162796,-1060653,-2925319,
%T A354395 30881760,598929239,5688937797,29126981516,-112222099065,
%U A354395 -4930674413971,-69798552313728,-598032658869829,-1296500625378255,65193402297999524,1515140106814565547
%N A354395 Expansion of e.g.f. exp( -(exp(x) - 1)^2 / 2 ).
%F A354395 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,2) * a(n-k).
%F A354395 a(n) = Sum_{k=0..floor(n/2)} (2*k)! * Stirling2(n,2*k)/((-2)^k * k!).
%o A354395 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(exp(x)-1)^2/2)))
%o A354395 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i-1, j-1)*stirling(j, 2, 2)*v[i-j+1])); v;
%o A354395 (PARI) a(n) = sum(k=0, n\2, (2*k)!*stirling(n, 2*k, 2)/((-2)^k*k!));
%Y A354395 Cf. A000587, A354396, A354397, A354398.
%Y A354395 Cf. A060311, A354391.
%K A354395 sign
%O A354395 0,4
%A A354395 _Seiichi Manyama_, May 25 2022