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 A376107 #10 Feb 16 2025 08:34:07
%S A376107 0,1,4,27,260,3265,50634,935263,20053816,489677697,13416375950,
%T A376107 407609962111,13600700469828,494442286466401,19452778285314178,
%U A376107 823489845351967935,37323572563440199664,1803303384581598518785,92523649833821902792086
%N A376107 Expansion of e.g.f. LambertW(x / (1 - 3*x)).
%H A376107 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376107 E.g.f. A(x) satisfies A(x) = x * (3*A(x) + exp(-A(x))).
%F A376107 E.g.f.: Series_Reversion( x / (3*x + exp(-x)) ).
%F A376107 a(n) = n! * Sum_{k=1..n} 3^(n-k) * (-k)^(k-1) * binomial(n-1,k-1)/k!.
%t A376107 nmax=20; CoefficientList[InverseSeries[Series[x / (3*x + E^(-x)), {x, 0, nmax}], x], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 20 2024 *)
%o A376107 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(x/(1-3*x)))))
%o A376107 (PARI) a(n) = n!*sum(k=1, n, 3^(n-k)*(-k)^(k-1)*binomial(n-1, k-1)/k!);
%Y A376107 Cf. A060356, A376106.
%Y A376107 Cf. A376101.
%K A376107 nonn
%O A376107 0,3
%A A376107 _Seiichi Manyama_, Sep 10 2024