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.

1, 3, 27, 339, 5067, 84738, 1536867, 29687772, 603835479, 12831704772, 283320533673, 6473430313902, 152586247226958, 3701535783215857, 92238331155559794, 2357440730629390878, 61720161749858023305

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

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.

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.

Example

G.f.: A(x) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 +...
A(x)^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 +...
A(x) = G(G(G(x))) where
G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 +...
Let F(x) = g.f. of A153852 and H(x) = g.f. of A153854, then
A(x) = F(x) + x^2*H(x)^3 where
F(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 +...
H(x) = x + 4*x^3 + 42*x^5 + 594*x^7 + 9827*x^9 +...
H(x)^3 = x^3 + 12*x^5 + 174*x^7 + 2854*x^9 + 51045*x^11 +...

Prog

(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)}

Crossrefs

Cf. A153851, A153852, A153854, A153850.

Sequence in context: A217363 A234462 A371657 * A067000 A354658 A307650

Adjacent sequences: A153850 A153851 A153852 * A153854 A153855 A153856

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2009

Status

approved