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 A377373 #19 Feb 16 2025 08:34:07
%S A377373 1,1,3,14,93,794,8335,103774,1496313,24525458,450478131,9166307798,
%T A377373 204692557333,4977320639290,130918278855351,3703846153114574,
%U A377373 112155490349101041,3619411771703973410,124011196515200953819,4496024219722304736070,171963129575721708667341
%N A377373 Expansion of e.g.f. (1/x) * Series_Reversion( x / (exp(-x) + 2*x) ).
%H A377373 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377373 E.g.f.: (1/x) * LambertW(x / (1 - 2*x)).
%F A377373 a(n) = n! * Sum_{k=0..n} (-1)^k * 2^(n-k) * (k+1)^(k-1) * binomial(n,k)/k!.
%F A377373 a(n) = A376106(n+1)/(n+1).
%o A377373 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(x/(1-2*x))/x))
%o A377373 (PARI) a(n) = n!*sum(k=0, n, (-1)^k*2^(n-k)*(k+1)^(k-1)*binomial(n, k)/k!);
%Y A377373 Cf. A108919, A377374.
%Y A377373 Cf. A376106.
%K A377373 nonn
%O A377373 0,3
%A A377373 _Seiichi Manyama_, Dec 28 2024