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 A362690 #25 Feb 16 2025 08:34:05
%S A362690 1,1,5,28,245,2816,40537,702976,14270153,332102656,8719631981,
%T A362690 255020847104,8222803663549,289815184113664,11085650268060929,
%U A362690 457386463819595776,20248713707077863953,957435459515190345728,48157934732749633188565
%N A362690 E.g.f. satisfies A(x) = exp(x^2 + x * A(x)).
%C A362690 Essentially the same as A138293.
%H A362690 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362690 E.g.f.: -LambertW(-x * exp(x^2)) / x = exp( x^2 - LambertW(-x*exp(x^2)) ).
%F A362690 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-k-1) / (k! * (n-2*k)!).
%F A362690 a(n) ~ sqrt(1 + LambertW(2*exp(-2))) * 2^((n+1)/2) * n^(n-1) / (exp(n) * LambertW(2*exp(-2))^((n+1)/2)). - _Vaclav Kotesovec_, Nov 10 2023
%o A362690 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2-lambertw(-x*exp(x^2)))))
%Y A362690 Cf. A349562, A362691.
%Y A362690 Cf. A125500, A138293, A362736.
%K A362690 nonn
%O A362690 0,3
%A A362690 _Seiichi Manyama_, May 01 2023