%I A158888
%S A158888 1,1,3,21,305,8785,497089,55504321,12305179649,5437293562113,
%T A158888 4797448178045953,8459278545576012801,29821007074850747998209,
%U A158888 210213196038821563873677313,2963378701144932768795387346945
%N A158888 G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(2^n*x)^n.
%C A158888 Compare g.f. to the g.f. C(x) of the Catalan numbers:
%C A158888 C(x) = Sum_{n>=0} x^n * C(x)^n.
%e A158888 G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 305*x^4 + 8785*x^5 +...
%e A158888 A(2x) = 1 + 2*x + 12*x^2 + 168*x^3 + 4880*x^4 + 281120*x^5 +...
%e A158888 A(4x)^2 = 1 + 8*x + 112*x^2 + 3072*x^3 + 169216*x^4 +...
%e A158888 A(8x)^3 = 1 + 24*x + 768*x^2 + 41984*x^3 + 4411392*x^4 +...
%e A158888 A(16x)^4 = 1 + 64*x + 4608*x^2 + 507904*x^3 + 102432768*x^4 +...
%e A158888 A(32x)^5 = 1 + 160*x + 25600*x^2 + 5734400*x^3 + 2233466880*x^4 +...
%o A158888 (PARI) {a(n)=local(A=1+x);for(n=2,n, A=sum(k=0,n,x^k*subst(A,x,x*2^k+x*O(x^n))^k));
               polcoeff(A,n)}
%Y A158888 Cf. A000108.
%Y A158888 Sequence in context: A126461 A000681 A055555 this_sequence A005329 A134528 
               A118410
%Y A158888 Adjacent sequences: A158885 A158886 A158887 this_sequence A158889 A158890 
               A158891
%K A158888 nonn
%O A158888 0,3
%A A158888 Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2009