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 A362391 #18 Feb 16 2025 08:34:05
%S A362391 1,1,1,4,25,121,751,7351,73417,749449,9477181,136883341,2041250641,
%T A362391 33289802833,608025141907,11815916748091,242532915013201,
%U A362391 5369303859003601,126896359555326745,3153096762426186553,82705881733348530241,2293511922269658189121
%N A362391 E.g.f. satisfies A(x) = exp(x + x^3/2 * A(x)).
%H A362391 Seiichi Manyama, <a href="/A362391/b362391.txt">Table of n, a(n) for n = 0..427</a>
%H A362391 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362391 E.g.f.: exp(x - LambertW(-x^3/2 * exp(x))) = -2 * LambertW(-x^3/2 * exp(x))/x^3.
%F A362391 a(n) = n! * Sum_{k=0..floor(n/3)} (1/2)^k * (k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o A362391 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/2*exp(x)))))
%Y A362391 Column k=3 of A362378.
%Y A362391 Cf. A362380, A362479.
%K A362391 nonn
%O A362391 0,4
%A A362391 _Seiichi Manyama_, Apr 20 2023