%I #5 Apr 28 2012 23:57:00

%S 1,1,4,30,324,4480,74544,1438808,31459536,766573668,20569553080,

%T 602290243456,19105119410064,652635503205608,23888307843434944,

%U 932847459551529600,38716407912891973504,1702050349577155752784,79018450946973490981176

%N G.f. satisfies: A(x) = x + x^2 * d/dx A(A(x)).

%F G.f. satisfies: A(x) = x + x^2 * A'(x) * A'(A(x)).

%e G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 324*x^5 + 4480*x^6 + 74544*x^7 +...

%e Related expansions:

%e A'(x) = 1 + 2*x + 12*x^2 + 120*x^3 + 1620*x^4 + 26880*x^5 + 521808*x^6 +...

%e A(A(x)) = x + 2*x^2 + 10*x^3 + 81*x^4 + 896*x^5 + 12424*x^6 + 205544*x^7 +...

%o (PARI) {a(n)=local(A=x+x^2+x*O(x^n));for(i=1,n,A=x+x^2*deriv(subst(A,x,A)));polcoeff(A,n)}

%o for(n=1,21,print1(a(n),", "))

%Y Cf. A211827.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Apr 21 2012