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%I #5 Jan 04 2024 18:17:38
%S 1,2,15,165,2213,33693,561867,10053141,190489374,3788856192,
%T 78613758564,1693737431667,37760673462507,868775517322730,
%U 20583609967109565,501340716386677815,12535093359045980151,321360932709750239226
%N Nonzero coefficients of g.f.: A(x) = G(G(x)) where G(x) = x + G(G(x))^3 is the g.f. of A153851.
%F G.f.: A(x) = Sum_{n>=0} a(2n+1)*x^(2n+1) = G(G(x)) where G(x) is the g.f. of A153851.
%F G.f.: A(x) = G(x) + G(G(G(x)))^3 where G(x) is the g.f. of A153851 and G(G(G(x))) is the g.f. of A153853.
%e G.f.: A(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 + ...
%e A(x)^3 = x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + 145815*x^13 + ...
%e A(x) = G(G(x)) where
%e G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + ...
%e Also, A(x) = G(x) + G(G(G(x)))^3 where G(G(G(x))) begins
%e G(G(G(x))) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 + 84738*x^11 + ... + A153853(n)*x^(2*n-1) + ...
%e G(G(G(x)))^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 + ...
%o (PARI) {a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(G,x,G), 2*n-1)}
%Y Cf. A153851, A153853, A153854, A153850.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jan 21 2009
%E Formula corrected by _Paul D. Hanna_, Dec 07 2009
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