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%I #4 Mar 30 2012 18:37:26
%S 1,1,2,7,36,243,2016,19745,222318,2824546,39938124,621808679,
%T 10569132576,194745803641,3866820606006,82313887902511,
%U 1870203518285750,45174881008705328,1156071783429567906,31246398342838909318
%N G.f. satisfies: A(x) = x + x*sqrt(A(A(x)) - A(x)).
%F Let F(x) be the g.f. of A185753, then g.f. A(x) satisfies:
%F * A(x) = x + (F(x)-1)^2,
%F * A(x) = x*F(A(x)),
%F * A(x) = Series_Reversion(x/F(x)).
%e G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 243*x^6 +...
%e A(A(x)) = x + 2*x^2 + 6*x^3 + 25*x^4 + 136*x^5 + 922*x^6 + 7524*x^7 +...
%e The g.f. of A185753 begins:
%e F(x) = 1 + x + x^2 + 3*x^3 + 15*x^4 + 102*x^5 + 861*x^6 + 8593*x^7 +...
%e where
%e (F(x)-1)^2 = x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 243*x^6 + 2016*x^7 +...
%e F(A(x)) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 243*x^5 + 2016*x^6 +...
%o (PARI) {a(n)=local(A=x+x^2);for(i=1,n,A=2*A-x-(x/serreverse(A+x*O(x^n))-1)^2);polcoeff(A,n)}
%Y Cf. A185753.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Feb 02 2011
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