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 A375394 #13 Aug 21 2024 11:22:10
%S A375394 1,1,3,12,63,420,3345,31080,330225,3946320,52401195,765404640,
%T A375394 12196214415,210533843520,3913845680745,77955813936000,
%U A375394 1656235524168225,37387344753158400,893615568162592275,22545399132243187200,598744483093370188575,16696076277239091532800
%N A375394 Expansion of e.g.f. 1 / (exp(-x^2/2) - x).
%F A375394 a(n) = n! * Sum_{k=0..floor(n/2)} ((n-2*k+1)/2)^k/k!.
%F A375394 a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / ((1 + LambertW(1)) * exp(n) * LambertW(1)^((n+1)/2)). - _Vaclav Kotesovec_, Aug 21 2024
%o A375394 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^2/2)-x)))
%o A375394 (PARI) a(n) = n!*sum(k=0, n\2, ((n-2*k+1)/2)^k/k!);
%Y A375394 Cf. A072597, A375395.
%K A375394 nonn
%O A375394 0,3
%A A375394 _Seiichi Manyama_, Aug 21 2024