A153854 Nonzero coefficients of g.f.: A(x) = G(G(G(G(x)))) where G(x) = x + G(G(x))^3 is the g.f. of A153851.

1, 4, 42, 594, 9827, 179928, 3545637, 73988631, 1618178067, 36832568283, 868184365137, 21113629246953, 528282055072773, 13569770211307323, 357215846155083585, 9623529095387448543, 265025641890780905892

Offset: 1

Author

Paul D. Hanna, Jan 21 2009

Keywords

• nonn

Examples

			G.f.: A(x) = x + 4*x^3 + 42*x^5 + 594*x^7 + 9827*x^9 +...
A(x)^3 = x^3 + 12*x^5 + 174*x^7 + 2854*x^9 + 51045*x^11 +...
A(x) = G(G(G(G(x)))) where
G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 +...
A(x) = F(F(x)) where F(x) = G(G(x)) is the g.f. of A153852:
F(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 + 33693*x^11 +...
		

Crossrefs

Cf. A153851, A153852, A153853, A153850.

Programs

PARI

{a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(subst(G,x,G),x,subst(G,x,G)), 2*n-1)}

Formula

G.f.: A(x) = Sum_{n>=0} a(2n+1)*x^(2n+1) = G(G(G(G(x)))) where G(x) is the g.f. of A153851.

G.f.: A(x) = F(F(x)) where F(x) is the g.f. of A153852.