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 A376098 #16 Feb 16 2025 08:34:07
%S A376098 0,1,6,66,1112,25640,753552,26950000,1136106624,55167345792,
%T A376098 3032389917440,186130732899584,12619351769121792,936591263680543744,
%U A376098 75527892444435486720,6575887645386829301760,614790327790529665138688,61429094739085165675446272
%N A376098 Expansion of e.g.f. -LambertW(-2*x / (1 - x))/2.
%H A376098 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A376098 E.g.f. A(x) satisfies A(x) = x * (A(x) + exp(2*A(x))).
%F A376098 E.g.f.: Series_Reversion( x / (x + exp(2*x)) ).
%F A376098 a(n) = n! * Sum_{k=1..n} (2*k)^(k-1) * binomial(n-1,k-1)/k!.
%F A376098 a(n) = n * A352448(n-1).
%F A376098 a(n) ~ (2 + exp(-1))^(n + 1/2) * n^(n-1) / 2^(3/2). - _Vaclav Kotesovec_, Sep 10 2024
%o A376098 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x/(1-x))/2)))
%o A376098 (PARI) a(n) = n!*sum(k=1, n, (2*k)^(k-1)*binomial(n-1, k-1)/k!);
%Y A376098 Cf. A052871, A376099.
%Y A376098 Cf. A352448, A376093.
%K A376098 nonn
%O A376098 0,3
%A A376098 _Seiichi Manyama_, Sep 10 2024