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 A346888 #21 May 13 2022 18:21:31
%S A346888 1,0,1,3,12,70,465,3591,31948,319068,3539385,43205635,575312826,
%T A346888 8298867798,128921967265,2145837600375,38097353658120,718657756980376,
%U A346888 14354000800751313,302625047150614179,6716038666999745710,156498725047355717250,3820426102008414736761
%N A346888 Expansion of e.g.f. 1 / (1 - x^2 * exp(x) / 2).
%H A346888 Seiichi Manyama, <a href="/A346888/b346888.txt">Table of n, a(n) for n = 0..442</a>
%F A346888 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * binomial(k,2) * a(n-k).
%F A346888 a(n) ~ n! / ((1 + LambertW(1/sqrt(2))) * 2^(n+1) * LambertW(1/sqrt(2))^n). - _Vaclav Kotesovec_, Aug 08 2021
%F A346888 a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k)/(2^k * (n-2*k)!). - _Seiichi Manyama_, May 13 2022
%t A346888 nmax = 22; CoefficientList[Series[1/(1 - x^2 Exp[x]/2), {x, 0, nmax}], x] Range[0, nmax]!
%t A346888 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, 2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]
%o A346888 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-x^2*exp(x)/2))) \\ _Michel Marcus_, Aug 06 2021
%o A346888 (PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/(2^k*(n-2*k)!)); \\ _Seiichi Manyama_, May 13 2022
%Y A346888 Column k=2 of A351703.
%Y A346888 Cf. A006153, A346889, A346890, A346893.
%Y A346888 Cf. A000217, A133189, A308946, A353998.
%K A346888 nonn
%O A346888 0,4
%A A346888 _Ilya Gutkovskiy_, Aug 06 2021