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%I #15 Oct 15 2019 12:20:30
%S 1,4,29,260,2603,27888,312828,3627492,43133255,523068260,6444287837,
%T 80433798640,1014906999988,12924812183200,165908765933928,
%U 2144416925372580,27885292408504863,364554713774523660,4788696579412309575,63171942535632208740,836566570704764498115
%N G.f. A(x) satisfies: x = A(x) * (1 - A(x)) * (1 - 3*A(x)).
%H Michael De Vlieger, <a href="/A250885/b250885.txt">Table of n, a(n) for n = 1..871</a>
%H 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.
%F G.f.: Series_Reversion(x - 4*x^2 + 3*x^3).
%F G.f. A(x) satisfies: x = -2*(1-A(x)) + 5*(1-A(x))^2 - 3*(1-A(x))^3.
%F a(n) ~ (7*sqrt(7)+10)^(n-1/2) / (sqrt(Pi) * 7^(1/4) * n^(3/2) * 2^(n+1/2)). - _Vaclav Kotesovec_, Aug 22 2017
%e G.f.: A(x) = x + 4*x^2 + 29*x^3 + 260*x^4 + 2603*x^5 + 27888*x^6 +...
%e Related expansions.
%e A(x)^2 = x^2 + 8*x^3 + 74*x^4 + 752*x^5 + 8127*x^6 + 91680*x^7 +...
%e A(x)^3 = x^3 + 12*x^4 + 135*x^5 + 1540*x^6 + 17964*x^7 + 213948*x^8 +...
%e where x = A(x) - 4*A(x)^2 + 3*A(x)^3.
%t Rest[CoefficientList[InverseSeries[Series[x - 4*x^2 + 3*x^3, {x, 0, 20}], x],x]] (* _Vaclav Kotesovec_, Aug 22 2017 *)
%o (PARI) {a(n)=polcoeff(serreverse(x - 4*x^2 + 3*x^3 + x^2*O(x^n)), n)}
%o for(n=1,30,print1(a(n),", "))
%K nonn
%O 1,2
%A _Paul D. Hanna_, Nov 28 2014
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