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 A362523 #17 Aug 05 2025 03:32:15
%S A362523 1,1,1,7,25,61,1201,7771,30577,1058905,9904321,53722351,2708688841,
%T A362523 33126146197,228967340785,15262865820931,230517745701601,
%U A362523 1936173471789361,161021598306402817,2894434429492525015,28614958982310290041
%N A362523 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) / (k! * (n-3*k)!).
%H A362523 Seiichi Manyama, <a href="/A362523/b362523.txt">Table of n, a(n) for n = 0..427</a>
%H A362523 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362523 E.g.f.: exp(x - LambertW(-x^3)) = -LambertW(-x^3)/x^3 * exp(x).
%F A362523 a(n) ~ sqrt(3) * (exp(3*exp(-1/3)/2) + 2*cos(sqrt(3)*exp(-1/3)/2 - 2*Pi*n/3)) * n^(n-1) / exp(2*n/3 + exp(-1/3)/2 - 1). - _Vaclav Kotesovec_, Aug 05 2025
%o A362523 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3))))
%Y A362523 Cf. A088957, A362522.
%Y A362523 Cf. A089464, A362348.
%K A362523 nonn,easy
%O A362523 0,4
%A A362523 _Seiichi Manyama_, Apr 23 2023