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 A362347 #19 Aug 05 2025 05:18:09
%S A362347 1,1,3,7,61,261,3991,24403,524217,4149001,114544171,1111976031,
%T A362347 37492210933,431097055117,17165526306111,228085258466731,
%U A362347 10472666396599921,157882659583461393,8211536252680154707,138474928851961700791,8045878340298511456941
%N A362347 a(n) = n! * Sum_{k=0..floor(n/2)} k^k / (k! * (n-2*k)!).
%H A362347 Winston de Greef, <a href="/A362347/b362347.txt">Table of n, a(n) for n = 0..414</a>
%H A362347 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362347 E.g.f.: exp(x) / (1 + LambertW(-x^2)).
%F A362347 a(n) ~ (exp(2*exp(-1/2)) + (-1)^n) * n^n / (sqrt(2) * exp(n/2 + exp(-1/2))). - _Vaclav Kotesovec_, Aug 05 2025
%o A362347 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2))))
%Y A362347 Cf. A086331, A362348, A362349.
%Y A362347 Cf. A277614.
%K A362347 nonn
%O A362347 0,3
%A A362347 _Seiichi Manyama_, Apr 17 2023