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A153853 Nonzero coefficients of g.f.: A(x) = G(G(G(x))) where G(x) = x + G(G(x))^3 is the g.f. of A153851.

%I A153853 #2 Mar 30 2012 18:37:15
%S A153853 1,3,27,339,5067,84738,1536867,29687772,603835479,12831704772,
%T A153853 283320533673,6473430313902,152586247226958,3701535783215857,
%U A153853 92238331155559794,2357440730629390878,61720161749858023305
%N A153853 Nonzero coefficients of g.f.: A(x) = G(G(G(x))) where G(x) = x + G(G(x))^3 is the g.f. of A153851.
%F A153853 G.f.: A(x) = Sum_{n>=0} a(2n+1)*x^(2n+1) = G(G(G(x))) where G(x) is the g.f. of A153851.
%F A153853 G.f.: A(x) = F(x) + x^2*H(x)^3 where F(x) is the g.f. of A153852 and H(x) is the g.f. of A153854.
%e A153853 G.f.: A(x) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 +...
%e A153853 A(x)^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 +...
%e A153853 A(x) = G(G(G(x))) where
%e A153853 G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 +...
%e A153853 Let F(x) = g.f. of A153852 and H(x) = g.f. of A153854, then
%e A153853 A(x) = F(x) + x^2*H(x)^3 where
%e A153853 F(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 +...
%e A153853 H(x) = x + 4*x^3 + 42*x^5 + 594*x^7 + 9827*x^9 +...
%e A153853 H(x)^3 = x^3 + 12*x^5 + 174*x^7 + 2854*x^9 + 51045*x^11 +...
%o A153853 (PARI) {a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(G,x,subst(G,x,G)), 2*n-1)}
%Y A153853 Cf. A153851, A153852, A153854, A153850.
%K A153853 nonn
%O A153853 1,2
%A A153853 _Paul D. Hanna_, Jan 21 2009