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 A362747 #15 Feb 16 2025 08:34:05
%S A362747 1,1,4,22,182,1996,27412,453160,8767516,194438800,4864250096,
%T A362747 135538060384,4163356010728,139784741268160,5093269640966704,
%U A362747 200170986137297536,8440841773833141008,380153135554220691712,18212499110682362677312
%N A362747 E.g.f. satisfies A(x) = exp(x^2/2 + x * A(x)).
%H A362747 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362747 E.g.f.: -LambertW(-x * exp(x^2/2)) / x = exp( x^2/2 - LambertW(-x*exp(x^2/2)) ).
%F A362747 a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-k-1) / (2^k * k! * (n-2*k)!).
%F A362747 a(n) ~ sqrt(1+LambertW(exp(-2))) * n^(n-1) / (exp(n)*LambertW(exp(-2))^((n+1)/2)). - _Vaclav Kotesovec_, Nov 10 2023
%o A362747 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/2-lambertw(-x*exp(x^2/2)))))
%Y A362747 Cf. A349562, A362748.
%Y A362747 Cf. A143740, A362690.
%K A362747 nonn
%O A362747 0,3
%A A362747 _Seiichi Manyama_, May 02 2023