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 A376099 #14 Feb 16 2025 08:34:07
%S A376099 0,1,8,123,2940,96465,4035438,205395687,12320780328,851216818977,
%T A376099 66565617543450,5812559883272439,560602050420898764,
%U A376099 59186681025383491281,6789351417468526481526,840843424588323640992615,111820607202879512913388752,15892724010727366554445999425
%N A376099 Expansion of e.g.f. -LambertW(-3*x / (1 - x))/3.
%H A376099 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376099 E.g.f. A(x) satisfies A(x) = x * (A(x) + exp(3*A(x))).
%F A376099 E.g.f.: Series_Reversion( x / (x + exp(3*x)) ).
%F A376099 a(n) = n! * Sum_{k=1..n} (3*k)^(k-1) * binomial(n-1,k-1)/k!.
%F A376099 a(n) ~ (3 + exp(-1))^(n + 1/2) * n^(n-1) / 3^(3/2). - _Vaclav Kotesovec_, Sep 10 2024
%o A376099 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-3*x/(1-x))/3)))
%o A376099 (PARI) a(n) = n!*sum(k=1, n, (3*k)^(k-1)*binomial(n-1, k-1)/k!);
%Y A376099 Cf. A052871, A376098.
%K A376099 nonn
%O A376099 0,3
%A A376099 _Seiichi Manyama_, Sep 10 2024