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%I #8 Aug 06 2014 20:13:45
%S 1,1,4,67,1769,62499,2718712,139232874,8166885453,538622419492,
%T 39414368809017,3167946276763685,277436199521729856,
%U 26298695327956996229,2683220559729561789860,293242531673596767855914,34182433657089947169431226,4234005174244450641927919376
%N G.f. satisfies: A(x)^3 = x + A(x*A(x)^3)^2.
%e G.f.: A(x) = 1 + x + 4*x^2 + 67*x^3 + 1769*x^4 + 62499*x^5 + 2718712*x^6 +...
%e RELATED SERIES.
%e A(x)^2 = 1 + 2*x + 9*x^2 + 142*x^3 + 3688*x^4 + 129072*x^5 + 5581063*x^6 +...
%e A(x)^3 = 1 + 3*x + 15*x^2 + 226*x^3 + 5769*x^4 + 199968*x^5 + 8594032*x^6 +...
%e A(x*A(x)^3) = 1 + x + 7*x^2 + 106*x^3 + 2754*x^4 + 96488*x^5 + 4175632*x^6 +...
%e A(x*A(x)^3)^2 = 1 + 2*x + 15*x^2 + 226*x^3 + 5769*x^4 + 199968*x^5 + 8594032*x^6 +...
%o (PARI) {a(n)=local(A=[1,1],Ax);for(i=1,n,A=concat(A,0);Ax=Ser(A);
%o A[#A]=Vec(1+subst(Ax^2,x,x*Ax^3) - Ax^3)[#A]);A[n+1]}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A240997, A240996.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 06 2014