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 A362301 #19 Feb 16 2025 08:34:05
%S A362301 1,1,1,19,97,301,13681,124951,647809,46543897,612367201,4447574011,
%T A362301 436897375201,7505523945349,70104150466897,8735878156045951,
%U A362301 185209511009456641,2114594302777738801,319284313084581674689,8053189772356178472547
%N A362301 a(n) = n! * Sum_{k=0..floor(n/3)} n^k * binomial(n-2*k,k)/(n-2*k)!.
%H A362301 Winston de Greef, <a href="/A362301/b362301.txt">Table of n, a(n) for n = 0..402</a>
%H A362301 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362301 a(n) = A362043(n,6*n).
%F A362301 a(n) = n! * [x^n] exp(x + n*x^3).
%F A362301 E.g.f.: exp( ( -LambertW(-3*x^3)/3 )^(1/3) ) / (1 + LambertW(-3*x^3)).
%F A362301 a(n) ~ (1 + 2*cos(2*Pi*mod(n,3)/3 - 3^(1/6)/2)*exp(-3^(2/3)/2)) * 3^(n/3 - 1/2) * n^n / exp(2*n/3 - 1/3^(1/3)). - _Vaclav Kotesovec_, Apr 18 2023
%o A362301 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-3*x^3)/3)^(1/3))/(1+lambertw(-3*x^3))))
%Y A362301 Cf. A362043.
%K A362301 nonn
%O A362301 0,4
%A A362301 _Seiichi Manyama_, Apr 15 2023