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 A375586 #7 Aug 20 2024 09:14:29
%S A375586 1,0,0,3,0,15,180,105,5040,46305,132300,3752595,33679800,243378135,
%T A375586 5565940380,56191160025,712410098400,14889814164225,183558878603100,
%U A375586 3236148386145675,66650136566013000,1027807726886515575,21983938825036488300,469896981350215644225
%N A375586 Expansion of e.g.f. 1 / (1 + x - x * exp(x^2/2)).
%F A375586 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(k,n-2*k)/(2^k*k!).
%o A375586 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2/2))))
%o A375586 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 2)/(2^k*k!));
%Y A375586 Cf. A052848, A375587.
%Y A375586 Cf. A375167.
%K A375586 nonn
%O A375586 0,4
%A A375586 _Seiichi Manyama_, Aug 19 2024