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 A295267 #15 Mar 27 2019 10:02:41
%S A295267 1,1,6,63,952,18885,465696,13764667,475039104,18767660553,
%T A295267 835805555200,41442148754391,2264776308946944,135268340058044557,
%U A295267 8767315076546568192,612911076907734961875,45973645939542007054336,3683096368557198711874833,313878687736263437290438656
%N A295267 Expansion of e.g.f. 2/(1 + sqrt(1 + 4*LambertW(-x))).
%H A295267 G. C. Greubel, <a href="/A295267/b295267.txt">Table of n, a(n) for n = 0..354</a>
%F A295267 E.g.f.: 1/(1 + LambertW(-x)/(1 + LambertW(-x)/(1 + LambertW(-x)/(1 + LambertW(-x)/(1 + ...))))), a continued fraction.
%F A295267 a(n) ~ 2^(2*n + 3/2) * n^(n-1) / (sqrt(3) * exp(3*n/4)). - _Vaclav Kotesovec_, Nov 19 2017
%p A295267 a:=series(2/(1+sqrt(1+4*LambertW(-x))),x=0,19): seq(n!*coeff(a,x,n),n=0..18); # _Paolo P. Lava_, Mar 27 2019
%t A295267 nmax = 18; CoefficientList[Series[2/(1 + Sqrt[1 + 4 LambertW[-x]]), {x, 0, nmax}], x] Range[0, nmax]!
%t A295267 nmax = 18; CoefficientList[Series[1/(1 + ContinuedFractionK[LambertW[-x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%o A295267 (PARI) x ='x+O('x^30); Vec(serlaplace(2/(1 +sqrt(1 +4*lambertw(-x))))) \\ _G. C. Greubel_, Jul 07 2018
%Y A295267 Cf. A000108, A180680, A277184, A295268.
%K A295267 nonn
%O A295267 0,3
%A A295267 _Ilya Gutkovskiy_, Nov 19 2017