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 A376106 #16 Feb 16 2025 08:34:07
%S A376106 0,1,2,9,56,465,4764,58345,830192,13466817,245254580,4955259441,
%T A376106 109995693576,2661003245329,69682488950060,1963774182830265,
%U A376106 59261538449833184,1906643335934717697,65149411890671521380,2356212733788818122561,89920484394446094721400
%N A376106 Expansion of e.g.f. LambertW(x / (1 - 2*x)).
%H A376106 Vaclav Kotesovec, <a href="/A376106/b376106.txt">Table of n, a(n) for n = 0..400</a>
%H A376106 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376106 E.g.f. A(x) satisfies A(x) = x * (2*A(x) + exp(-A(x))).
%F A376106 E.g.f.: Series_Reversion( x / (2*x + exp(-x)) ).
%F A376106 a(n) = n! * Sum_{k=1..n} 2^(n-k) * (-k)^(k-1) * binomial(n-1,k-1)/k!.
%t A376106 nmax=20; CoefficientList[InverseSeries[Series[x / (2*x + E^(-x)), {x, 0, nmax}], x], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 20 2024 *)
%o A376106 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(lambertw(x/(1-2*x)))))
%o A376106 (PARI) a(n) = n!*sum(k=1, n, 2^(n-k)*(-k)^(k-1)*binomial(n-1, k-1)/k!);
%Y A376106 Cf. A060356, A376107.
%Y A376106 Cf. A376100.
%K A376106 nonn
%O A376106 0,3
%A A376106 _Seiichi Manyama_, Sep 10 2024