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A250886 G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 2*A(x)).

%I A250886 #18 Oct 15 2019 12:20:52
%S A250886 1,1,4,15,68,322,1608,8283,43780,235950,1291992,7167030,40192488,
%T A250886 227488900,1297845008,7455558675,43088726148,250362137590,
%U A250886 1461641062200,8569690323810,50438119336440,297896152159260,1765010252344560,10487875429825950,62485899131628648,373198022044163532
%N A250886 G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 2*A(x)).
%H A250886 Michael De Vlieger, <a href="/A250886/b250886.txt">Table of n, a(n) for n = 1..1254</a>
%H A250886 Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H A250886 Thomas M. Richardson, <a href="http://arxiv.org/abs/1609.01193">The three 'R's and the Riordan dual</a>, arXiv:1609.01193 [math.CO], 2016.
%F A250886 G.f.: Series_Reversion(x - x^2 - 2*x^3).
%F A250886 G.f. A(x) satisfies: x = -3*(1+A(x)) + 5*(1+A(x))^2 - 2*(1+A(x))^3.
%F A250886 a(n) ~ 2^(n - 3/2) * (10 + 7*sqrt(7))^(n - 1/2) / (7^(1/4) * sqrt(Pi) * n^(3/2) * 3^(2*n - 1)). - _Vaclav Kotesovec_, Aug 22 2017
%e A250886 G.f.: A(x) = x + x^2 + 4*x^3 + 15*x^4 + 68*x^5 + 322*x^6 + 1608*x^7 + ...
%e A250886 Related expansions.
%e A250886 A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 38*x^5 + 182*x^6 + 900*x^7 + 4629*x^8 + ...
%e A250886 A(x)^3 = x^3 + 3*x^4 + 15*x^5 + 70*x^6 + 354*x^7 + 1827*x^8 + 9691*x^9 + ...
%e A250886 where x = A(x) - A(x)^2 - 2*A(x)^3.
%t A250886 Rest[CoefficientList[InverseSeries[Series[x - x^2 - 2*x^3, {x, 0, 20}], x],x]] (* _Vaclav Kotesovec_, Aug 22 2017 *)
%o A250886 (PARI) {a(n)=polcoeff(serreverse(x - x^2 - 2*x^3 + x^2*O(x^n)), n)}
%o A250886 for(n=1,30,print1(a(n),", "))
%K A250886 nonn
%O A250886 1,3
%A A250886 _Paul D. Hanna_, Nov 28 2014