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 A376101 #14 Feb 16 2025 08:34:07
%S A376101 0,1,8,99,1684,36865,994986,32106655,1209994808,52281293697,
%T A376101 2551380861070,138903509144191,8350198884092484,549502839975044449,
%U A376101 39295464010757324930,3034457861009541582015,251666093876245502584816,22310882229970705663827457
%N A376101 Expansion of e.g.f. -LambertW(-x / (1 - 3*x)).
%H A376101 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376101 E.g.f. A(x) satisfies A(x) = x * (3*A(x) + exp(A(x))).
%F A376101 E.g.f.: Series_Reversion( x / (3*x + exp(x)) ).
%F A376101 a(n) = n! * Sum_{k=1..n} 3^(n-k) * k^(k-1) * binomial(n-1,k-1)/k!.
%F A376101 a(n) ~ (1 + 3*exp(-1))^(n + 1/2) * n^(n-1). - _Vaclav Kotesovec_, Sep 10 2024
%o A376101 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x/(1-3*x)))))
%o A376101 (PARI) a(n) = n!*sum(k=1, n, 3^(n-k)*k^(k-1)*binomial(n-1, k-1)/k!);
%Y A376101 Cf. A052871, A376100.
%K A376101 nonn
%O A376101 0,3
%A A376101 _Seiichi Manyama_, Sep 10 2024