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G.f.: A(x) = G(G(x)) = G(x)*[1 + A(A(x))] where G(x) = x + x*G(G(G(x))) = g.f. of A091713.
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%I #2 Mar 30 2012 18:37:10

%S 1,2,8,46,330,2756,25782,263866,2909092,34181138,424730866,5549236120,

%T 75895955810,1082808876274,16069706031016,247501424330182,

%U 3948322598675930,65130737179097436,1109339652229852966

%N G.f.: A(x) = G(G(x)) = G(x)*[1 + A(A(x))] where G(x) = x + x*G(G(G(x))) = g.f. of A091713.

%F G.f. A(x) satisfies: G( x/(1 + A(x)) ) = x where G(x) = g.f. of A091713.

%e G.f.: A(x) = G(G(x)) such that G(x) = A(x)/[1 + A(A(x))] where

%e G(x) = x + x^2 + 3*x^3 + 15*x^4 + 99*x^5 + 781*x^6 + 7001*x^7 +...

%e A(x) = x + 2*x^2 + 8*x^3 + 46*x^4 + 330*x^5 + 2756*x^6 + 25782*x^7 +...

%e A(A(x)) = x + 4*x^2 + 24*x^3 + 180*x^4 + 1564*x^5 + 15140*x^6 +...

%o (PARI) {a(n)=local(A); A=x+x^2; for(i=3, n, A=x+x*subst(A, x, subst(A, x, A))+x*O(x^n)); polcoeff(subst(A, x, A), n, x)}

%Y Cf. A091713.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 04 2008