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 A362350 #17 Feb 16 2025 08:34:05
%S A362350 1,1,2,4,19,71,601,3277,39089,277489,4250341,37110701,693581197,
%T A362350 7184750509,158461520309,1899055549861,48269252293201,656869268651537,
%U A362350 18903165795857089,287927838327392929,9252988524143245181,155954097639111859501
%N A362350 a(n) = n! * Sum_{k=0..floor(n/2)} (k/2)^k / (k! * (n-2*k)!).
%H A362350 Winston de Greef, <a href="/A362350/b362350.txt">Table of n, a(n) for n = 0..437</a>
%H A362350 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362350 E.g.f.: exp(x) / (1 + LambertW(-x^2/2)).
%F A362350 a(n) ~ (exp(2^(3/2)*exp(-1/2)) + (-1)^n) * n^n / (2^((n+1)/2) * exp(n/2 + sqrt(2)*exp(-1/2))). - _Vaclav Kotesovec_, Apr 18 2023
%o A362350 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2/2))))
%Y A362350 Cf. A362351, A362352.
%Y A362350 Cf. A277614.
%K A362350 nonn
%O A362350 0,3
%A A362350 _Seiichi Manyama_, Apr 17 2023