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 A372159 #15 Feb 16 2025 08:34:06
%S A372159 1,3,21,216,2937,49788,1013247,24106134,657277185,20225122632,
%T A372159 693755934159,26261393088978,1087866116802081,48965716033901436,
%U A372159 2380245527593532559,124300353332797939422,6941285402232405794817,412817223292008085699344
%N A372159 E.g.f. A(x) satisfies A(x) = exp( 3 * x * A(x)^(1/3) / (1 - x) ).
%H A372159 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372159 E.g.f.: A(x) = exp( -3 * LambertW(-x / (1-x)) ).
%F A372159 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(n+(s-1)*k-1,n-k)/k!.
%o A372159 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-3*lambertw(-x/(1-x)))))
%o A372159 (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(n+(s-1)*k-1, n-k)/k!);
%Y A372159 Cf. A052868, A372158.
%K A372159 nonn
%O A372159 0,2
%A A372159 _Seiichi Manyama_, Apr 20 2024