A138913 G.f. A(x) satisfies: 4*A(x) = A(A(A(x))) + 3*x + x^2 with A(0)=0.

1, 1, 6, 99, 2362, 70484, 2463460, 97309959, 4251047468, 202470323828, 10409697289888, 573563068625768, 33682595044746416, 2099111839596600644, 138339363094940014088, 9612941947359915802978, 702527738704990333954432

Offset: 1

Author

Paul D. Hanna, Apr 03 2008

Keywords

• nonn

Comments

A(A(A(x))) is the 3rd self-composition of the g.f. A(x).

Examples

			G.f.: A(x) = x + x^2 + 6*x^3 + 99*x^4 + 2362*x^5 + 70484*x^6 +...
A(A(x)) = x + 2*x^2 + 14*x^3 + 229*x^4 + 5456*x^5 + 162710*x^6 +...
A(A(A(x))) = x + 3*x^2 + 24*x^3 + 396*x^4 + 9448*x^5 + 281936*x^6 +...
so that 4*A(x) = A(A(A(x))) + 3*x + x^2.
		

Crossrefs

Cf. A138739, A138914, A138915, A138916.

Programs

PARI

{a(n)=local(A=x+x^2);if(n<1,0, for(i=3,n+1,A=A+polcoeff(subst(A,x,subst(A,x,A+x*O(x^i))),i)*x^i); polcoeff(A,n))}