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 A377374 #15 Feb 16 2025 08:34:07
%S A377374 1,2,9,65,653,8439,133609,2506727,54408633,1341637595,37055451101,
%T A377374 1133391705819,38034022035877,1389484163236727,54899323023464529,
%U A377374 2332723285215012479,106076669681270501105,5140202768545661266227,264427503283923495485221,14392750805365239040586051
%N A377374 Expansion of e.g.f. (1/x) * Series_Reversion( x / (exp(-x) + 3*x) ).
%H A377374 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377374 E.g.f.: (1/x) * LambertW(x / (1 - 3*x)).
%F A377374 a(n) = n! * Sum_{k=0..n} (-1)^k * 3^(n-k) * (k+1)^(k-1) * binomial(n,k)/k!.
%F A377374 a(n) = A376107(n+1)/(n+1).
%o A377374 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(x/(1-3*x))/x))
%o A377374 (PARI) a(n) = n!*sum(k=0, n, (-1)^k*3^(n-k)*(k+1)^(k-1)*binomial(n, k)/k!);
%Y A377374 Cf. A108919, A377373.
%Y A377374 Cf. A376107.
%K A377374 nonn
%O A377374 0,2
%A A377374 _Seiichi Manyama_, Dec 28 2024