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 A375604 #24 May 01 2025 12:54:09
%S A375604 1,1,4,18,108,840,7680,82320,1009680,13910400,213071040,3589850880,
%T A375604 65975152320,1313624632320,28166959941120,647099547494400,
%U A375604 15857424488505600,412878579034521600,11382450106662835200,331230511848421785600,10146149192841050188800
%N A375604 Expansion of e.g.f. 1 / (exp(-x^2) - x).
%F A375604 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^k/k!.
%F A375604 a(n) ~ sqrt(Pi) * 2^(n/2 + 1) * n^(n + 1/2) / ((1 + LambertW(2)) * exp(n) * LambertW(2)^((n+1)/2)). - _Vaclav Kotesovec_, Aug 21 2024
%t A375604 With[{nn=20},CoefficientList[Series[1/(Exp[-x^2]-x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 01 2025 *)
%o A375604 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^2)-x)))
%o A375604 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)^k/k!);
%Y A375604 Cf. A072597, A375607.
%Y A375604 Cf. A375394, A375608.
%K A375604 nonn
%O A375604 0,3
%A A375604 _Seiichi Manyama_, Aug 21 2024