%I A121687
%S A121687 1,1,3,14,83,574,4432,37244,335153,3194510,32001596,335019839,
%T A121687 3649450270,41227610316,481724831132,5809341783543,72177761136925,
%U A121687 922539273876404,12115001489115910,163284755614174305
%N A121687 G.f. satisfies: A(x) = 1 + x*A(x) * A( x*A(x) )^2.
%F A121687 G.f. satisfies: G(x) = x/(1 + x*A(x)^2) where G(x*A(x)) = x.
%F A121687 G.f. satisfies: A(x) = 1/(1 - x*A(x*A(x))^2).
%e A121687 G.f. A(x) = 1 + x + 3*x^2 + 14*x^3 + 83*x^4 + 574*x^5 + 4432*x^6 +...
%e A121687 A(x)^2 = 1 + 2*x + 7*x^2 + 34*x^3 + 203*x^4 + 1398*x^5 + 10706*x^6 +...
%e A121687 A(x*A(x)) = 1 + x + 4*x^2 + 23*x^3 + 160*x^4 + 1259*x^5 + 10833*x^6 +...
%e A121687 A(x*A(x))^2 = 1 + 2*x + 9*x^2 + 54*x^3 + 382*x^4 + 3022*x^5 + 25993*x^6 
               +...
%e A121687 A(x)*A(x*A(x))^2 = 1 + 3*x + 14*x^2 + 83*x^3 + 574*x^4 + 4432*x^5 +...
%o A121687 (PARI) {a(n)=local(A=1+x);for(i=0,n,A=serreverse(x/(1+x*(A +x*O(x^n))^2))/
               x); polcoeff(A,n)}
%o A121687 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1/(1-x*subst(A^2,x,x*A)));
               polcoef f(A,n)}
%Y A121687 Sequence in context: A032080 A020104 A103467 this_sequence A154757 A074535 
               A005700
%Y A121687 Adjacent sequences: A121684 A121685 A121686 this_sequence A121688 A121689 
               A121690
%K A121687 nonn
%O A121687 0,3
%A A121687 Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2006, Aug 20 2008