%I #5 Mar 30 2012 18:37:27
%S 1,1,2,6,23,105,556,3409,24664,218686,2499812,38628853,829097387,
%T 24849303505,1035428836952,59712082983706,4754866838971645,
%U 522450200091413797,79208256385834752898,16575527137487435275695
%N G.f. A(x) satisfies: A(x)^2 = Sum_{n>=0} x^n*A(x)^(2^n).
%F G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(2^n-1).
%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 105*x^5 + 556*x^6 +...
%e which satisfies:
%e A(x)^2 = A(x) + x*A(x)^2 + x^2*A(x)^4 + x^3*A(x)^8 + x^4*A(x)^16 +...
%e where:
%e A(x)^2 = 1 + 2*x + 5*x^2 + 16*x^3 + 62*x^4 + 280*x^5 + 1450*x^6 + 8626*x^7 +...
%e A(x)^4 = 1 + 4*x + 14*x^2 + 52*x^3 + 213*x^4 + 968*x^5 + 4896*x^6 + 27836*x^7 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0,n,x^m*(A+x*O(x^n))^(2^m-1)));polcoeff(A,n)}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 27 2011