A153852 Nonzero coefficients of g.f.: A(x) = G(G(x)) where G(x) = x + G(G(x))^3 is the g.f. of A153851.

1, 2, 15, 165, 2213, 33693, 561867, 10053141, 190489374, 3788856192, 78613758564, 1693737431667, 37760673462507, 868775517322730, 20583609967109565, 501340716386677815, 12535093359045980151, 321360932709750239226

Offset: 1

Author

Paul D. Hanna, Jan 21 2009

Keywords

• nonn

Examples

			G.f.: A(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 + ...
A(x)^3 = x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + 145815*x^13 + ...
A(x) = G(G(x)) where
G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + ...
Also, A(x) = G(x) + G(G(G(x)))^3 where G(G(G(x))) begins
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) + ...
G(G(G(x)))^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 + ...
		

Crossrefs

Cf. A153851, A153853, A153854, A153850.

Programs

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)}

Formula

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.

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.

Extensions

Formula corrected by Paul D. Hanna, Dec 07 2009