A138913 - OEIS

%I #4 Mar 13 2015 23:32:34

%S 1,1,6,99,2362,70484,2463460,97309959,4251047468,202470323828,

%T 10409697289888,573563068625768,33682595044746416,2099111839596600644,

%U 138339363094940014088,9612941947359915802978,702527738704990333954432

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

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

%e G.f.: A(x) = x + x^2 + 6*x^3 + 99*x^4 + 2362*x^5 + 70484*x^6 +...

%e A(A(x)) = x + 2*x^2 + 14*x^3 + 229*x^4 + 5456*x^5 + 162710*x^6 +...

%e A(A(A(x))) = x + 3*x^2 + 24*x^3 + 396*x^4 + 9448*x^5 + 281936*x^6 +...

%e so that 4*A(x) = A(A(A(x))) + 3*x + x^2.

%o (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))}

%Y Cf. A138739, A138914, A138915, A138916.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Apr 03 2008