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 A362390 #21 Feb 16 2025 08:34:05
%S A362390 1,1,1,3,17,81,441,3641,33825,318753,3505521,45095601,616484001,
%T A362390 9013086369,145909533225,2556431401161,47388760825281,937507626246081,
%U A362390 19840711661183457,443937299529447009,10456231167451597761,259738234024404363201
%N A362390 E.g.f. satisfies A(x) = exp(x + x^3/3 * A(x)).
%H A362390 Seiichi Manyama, <a href="/A362390/b362390.txt">Table of n, a(n) for n = 0..434</a>
%H A362390 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362390 E.g.f.: exp(x - LambertW(-x^3/3 * exp(x))) = -3 * LambertW(-x^3/3 * exp(x))/x^3.
%F A362390 a(n) = n! * Sum_{k=0..floor(n/3)} (1/3)^k * (k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o A362390 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/3*exp(x)))))
%Y A362390 Column k=2 of A362378.
%Y A362390 Cf. A001470, A362478.
%K A362390 nonn
%O A362390 0,4
%A A362390 _Seiichi Manyama_, Apr 20 2023