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%I #6 Apr 13 2019 08:09:47
%S 1,0,0,1,0,1,4,1,10,23,18,92,168,241,856,1480,2904,8266,14854,33496,
%T 83578,161047,380488,884326,1819714,4321045,9730466,21019404,49456092,
%U 110408981,246005440,572574553,1281705752,2906696339,6711882928,15128432758,34625418170
%N G.f. A(x) satisfies: A(x) = (1 - x^2*A(x)^2)/(1 - x^2*A(x)^2 - x^3*A(x)^3).
%F G.f. A(x) satisfies: A(x) = Sum_{k>=0} A000931(k)*x^k*A(x)^k.
%F G.f.: A(x) = (1/x)*Series_Reversion(x*(1 - x^2 - x^3)/(1 - x^2)).
%e G.f.: A(x) = 1 + x^3 + x^5 + 4*x^6 + x^7 + 10*x^8 + 23*x^9 + 18*x^10 + 92*x^11 + 168*x^12 + ...
%t terms = 37; CoefficientList[1/x InverseSeries[Series[x (1 - x^2 - x^3)/(1 - x^2), {x, 0, terms}], x], x]
%t terms = 36; A[_] = 0; Do[A[x_] = (1 - x^2 A[x]^2)/(1 - x^2 A[x]^2 - x^3 A[x]^3) + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]
%t terms = 37; p[n_] := p[n] = SeriesCoefficient[(1 - x^2)/(1 - x^2 - x^3), {x, 0, n}]; A[_] = 1; Do[A[x_] = Sum[p[k] x^k A[x]^k, {k, 0, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%Y Cf. A000931, A049124, A049140, A067955, A307411, A307412, A307413, A307528.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Apr 12 2019
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