%I #5 Sep 26 2012 11:56:29

%S 1,2,6,26,146,978,7454,62882,576914,5687506,59732838,664040698,

%T 7775333858,95517840738,1227175022334,16444901577858,229338157229154,

%U 3321917275376098,49890293296044806,775682898796646810

%N G.f. satisfies: A(x) = x + x*A(x) + x*A(A(x)).

%F G.f. satisfies: A(x) = (1/x)*Series_Reversion( x/(1+x + x*A(x)) ).

%e A(x) = x + 2*x^2 + 6*x^3 + 26*x^4 + 146*x^5 + 978*x^6 + 7454*x^7 +...

%e A(A(x)) = x + 4*x^2 + 20*x^3 + 120*x^4 + 832*x^5 + 6476*x^6 +...

%o (PARI) {a(n)=local(F=x+x*O(x^n),G=F);for(i=1,n,F=x+x*F+x*subst(F,x,F));polcoeff(F,n)}

%Y Cf. A120575.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 15 2006