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 A362300 #31 Feb 16 2025 08:34:05
%S A362300 1,1,1,7,33,101,1681,14211,72577,1906633,23242401,166218911,
%T A362300 5966236321,95016917997,873707885233,39767572858651,781865428682241,
%U A362300 8787169718273681,484500265577706817,11335266937098816183,150554918241183405601,9749671976020428623221
%N A362300 a(n) = n! * Sum_{k=0..floor(n/3)} (n/3)^k * binomial(n-2*k,k)/(n-2*k)!.
%C A362300 Let k be a positive integer. It appears that reducing this sequence modulo k produces an eventually periodic sequence with period a multiple of k. For example, modulo 9 the sequence becomes [1, 1, 1, 7, 6, 2, 7, 0, 1, 1, 0, 8, 7, 0, 7, 7, 0, 8, 1, 0, 1, 7, 0, 2, 7, 0, 1, 1, 0, 8, 7, 0, 7, 7, 0, 8, 1, 0, 1, 7, 0, 2, 7, 0, 1, ...], with an apparent period [2, 7, 0, 1, 1, 0, 8, 7, 0, 7, 7, 0, 8, 1, 0, 1, 7, 0] of length 18 starting at a(5). - _Peter Bala_, Apr 16 2023
%H A362300 Winston de Greef, <a href="/A362300/b362300.txt">Table of n, a(n) for n = 0..425</a>
%H A362300 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362300 a(n) = A362043(n,2*n).
%F A362300 a(n) = n! * [x^n] exp(x + n*x^3/3).
%F A362300 E.g.f.: exp( ( -LambertW(-x^3) )^(1/3) ) / (1 + LambertW(-x^3)).
%F A362300 a(n) ~ (1 + 2*cos(2*Pi*mod(n,3)/3 - sqrt(3)/2)/exp(3/2)) * n^n / (sqrt(3) * exp(2*n/3 - 1)). - _Vaclav Kotesovec_, Apr 18 2023
%o A362300 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-x^3))^(1/3))/(1+lambertw(-x^3))))
%Y A362300 Cf. A362043, A362293.
%Y A362300 Cf. A277614, A362314, A362319.
%K A362300 nonn
%O A362300 0,4
%A A362300 _Seiichi Manyama_, Apr 15 2023