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 A358080 #17 May 01 2023 09:25:20
%S A358080 1,0,2,6,36,260,2190,21882,248696,3181320,45229050,707208590,
%T A358080 12063902532,222939837276,4436813677478,94605994108290,
%U A358080 2151763873634160,51999544476324752,1330540380342907506,35936656483848501654,1021700660649312689660
%N A358080 Expansion of e.g.f. 1/(1 - x^2 * exp(x)).
%H A358080 Seiichi Manyama, <a href="/A358080/b358080.txt">Table of n, a(n) for n = 0..425</a>
%F A358080 a(n) = n! * Sum_{k=0..floor(n/2)} k^(n - 2*k)/(n - 2*k)!.
%F A358080 a(n) ~ n! / ((1 + LambertW(1/2)) * 2^(n+1) * LambertW(1/2)^n). - _Vaclav Kotesovec_, Oct 30 2022
%o A358080 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^2*exp(x))))
%o A358080 (PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/(n-2*k)!);
%Y A358080 Cf. A006153, A358081.
%Y A358080 Cf. A216507, A345747, A358064.
%K A358080 nonn,easy
%O A358080 0,3
%A A358080 _Seiichi Manyama_, Oct 30 2022