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 A372234 #21 Feb 16 2025 08:34:06
%S A372234 1,2,4,20,160,1112,9424,114788,1453792,19242224,309179104,5533486268,
%T A372234 102733943536,2105041949480,47732237414320,1139969559931028,
%U A372234 28924667996076736,792458458301707232,22984740550326524608,699915806697250558316
%N A372234 E.g.f. A(x) satisfies A(x) = exp( 2 * x * (1 + x^2 * A(x)^(1/2)) ).
%H A372234 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372234 E.g.f.: A(x) = exp( 2*x - 2*LambertW(-x^3 * exp(x)) ).
%F A372234 a(n) = 2 * n! * Sum_{k=0..floor(n/3)} (k+2)^(n-2*k-1) / (k! * (n-3*k)!).
%F A372234 a(n) ~ 2*sqrt(1 + LambertW(exp(-1/3)/3)) * n^(n-1) / (3^(n + 11/2) * exp(n) * LambertW(exp(-1/3)/3)^(n+6)). - _Vaclav Kotesovec_, Jun 01 2024
%o A372234 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*x-2*lambertw(-x^3*exp(x)))))
%o A372234 (PARI) a(n) = 2*n!*sum(k=0, n\3, (k+2)^(n-2*k-1)/(k!*(n-3*k)!));
%Y A372234 Cf. A362392, A372156.
%K A372234 nonn
%O A372234 0,2
%A A372234 _Seiichi Manyama_, Apr 23 2024