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 A375591 #8 Aug 20 2024 09:14:21
%S A375591 1,0,0,3,0,15,90,105,2520,8505,66150,634095,3118500,40675635,
%T A375591 285675390,2896618725,31556725200,281774718225,3691224687150,
%U A375591 37783760189175,483465043561500,6108282465360075,76126660317858150,1102221773079151725,14598579860502838200
%N A375591 Expansion of e.g.f. exp( x * (exp(x^2/2) - 1) ).
%F A375591 a(n) = n! * Sum_{k=0..floor(n/2)} Stirling2(k,n-2*k)/(2^k*k!).
%o A375591 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)-1))))
%o A375591 (PARI) a(n) = n!*sum(k=0, n\2, stirling(k, n-2*k, 2)/(2^k*k!));
%Y A375591 Cf. A052506, A375592.
%Y A375591 Cf. A357966, A375586.
%K A375591 nonn
%O A375591 0,4
%A A375591 _Seiichi Manyama_, Aug 19 2024