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 A372155 #14 Feb 16 2025 08:34:06
%S A372155 1,3,21,198,2505,39348,743967,16465494,418281393,12006610344,
%T A372155 384595471119,13607063765298,527217367699881,22209587195328588,
%U A372155 1010947593782034687,49457001919808733102,2588247541696766293857,144302243002459116148944
%N A372155 E.g.f. A(x) satisfies A(x) = exp( 3 * x * (1 + x) * A(x)^(1/3) ).
%H A372155 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372155 E.g.f.: A(x) = exp( -3 * LambertW(-x * (1+x)) ).
%F A372155 If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(s*k,n-k)/k!.
%o A372155 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-3*lambertw(-x*(1+x)))))
%o A372155 (PARI) a(n, r=3, s=1, t=1, u=0) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);
%Y A372155 Cf. A362771, A372154.
%K A372155 nonn
%O A372155 0,2
%A A372155 _Seiichi Manyama_, Apr 20 2024