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A250887 G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 3*A(x)).

%I A250887 #16 Oct 15 2019 12:21:12
%S A250887 1,2,11,70,503,3864,31092,258654,2206655,19200610,169739843,
%T A250887 1520241320,13764959908,125792608400,1158745944312,10747830197070,
%U A250887 100295912869263,940958196049830,8870071185895425,83972749650989430,798033019890224415,7610570090722324320,72810031747355657040
%N A250887 G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 3*A(x)).
%H A250887 Michael De Vlieger, <a href="/A250887/b250887.txt">Table of n, a(n) for n = 1..995</a>
%H A250887 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 A250887 Thomas M. Richardson, <a href="http://arxiv.org/abs/1609.01193">The three 'R's and Dual Riordan Arrays</a>, arXiv:1609.01193 [math.CO], 2016.
%F A250887 G.f.: Series_Reversion(x - 2*x^2 - 3*x^3).
%F A250887 a(n) ~ (13*sqrt(13) + 35)^(n-1/2) / (13^(1/4) * sqrt(Pi) * n^(3/2) * 2^(3*n-1/2)). - _Vaclav Kotesovec_, Aug 21 2017
%e A250887 G.f.: A(x) = x + 2*x^2 + 11*x^3 + 70*x^4 + 503*x^5 + 3864*x^6 + ...
%e A250887 Related expansions.
%e A250887 A(x)^2 = x^2 + 4*x^3 + 26*x^4 + 184*x^5 + 1407*x^6 + 11280*x^7 + ...
%e A250887 A(x)^3 = x^3 + 6*x^4 + 45*x^5 + 350*x^6 + 2844*x^7 + 23814*x^8 + ...
%e A250887 where x = A(x) - 2*A(x)^2 - 3*A(x)^3.
%e A250887 The square-root of A(x)/x is the g.f. of A222050:
%e A250887 sqrt(A(x)/x) = 1 + x + 5*x^2 + 30*x^3 + 209*x^4 + 1573*x^5 + 12478*x^6 + ...
%t A250887 Rest[CoefficientList[InverseSeries[Series[x - 2*x^2 - 3*x^3, {x, 0, 20}], x], x]] (* _Vaclav Kotesovec_, Aug 21 2017 *)
%o A250887 (PARI) {a(n)=polcoeff(serreverse(x - 2*x^2 - 3*x^3 + x^2*O(x^n)),n)}
%o A250887 for(n=1,30,print1(a(n),", "))
%Y A250887 Cf. A222050.
%K A250887 nonn
%O A250887 1,2
%A A250887 _Paul D. Hanna_, Nov 28 2014