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 A372334 #17 Feb 16 2025 08:34:06
%S A372334 0,1,8,102,2092,60140,2220954,100119670,5328468968,326960686872,
%T A372334 22724388453070,1764411577328906,151364204180518476,
%U A372334 14217940294767407380,1451334877597451677250,159972528561402504191190,18936257811933773637390544,2395818853376147403857700656
%N A372334 Expansion of e.g.f. -exp(x) * LambertW(-3*x)/3.
%H A372334 Seiichi Manyama, <a href="/A372334/b372334.txt">Table of n, a(n) for n = 0..334</a>
%H A372334 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A372334 a(n) = Sum_{k=1..n} (3*k)^(k-1) * binomial(n,k).
%F A372334 G.f.: Sum_{k>=1} (3*k)^(k-1) * x^k / (1-x)^(k+1).
%F A372334 a(n) ~ exp(exp(-1)/3) * 3^(n-1) * n^(n-1). - _Vaclav Kotesovec_, Apr 30 2024
%o A372334 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-3*x)/3)))
%o A372334 (PARI) a(n) = sum(k=1, n, (3*k)^(k-1)*binomial(n, k));
%Y A372334 Cf. A277473, A372333.
%Y A372334 Cf. A372316.
%K A372334 nonn
%O A372334 0,3
%A A372334 _Seiichi Manyama_, Apr 28 2024