A138914 - OEIS

%I #4 Mar 14 2015 10:13:17

%S 1,1,12,390,18304,1071862,73349996,5661162666,482252816998,

%T 44704184452202,4465265748489708,477159108766899654,

%U 54255973609630750372,6536766146592886952548,831617552461457925554152

%N G.f. A(x) satisfies: 5*A(x) = A(A(A(A(x)))) + 4*x + x^2 with A(0)=0.

%C A(A(A(A(x)))) is the 4th self-composition of the g.f. A(x).

%e G.f.: A(x) = x + x^2 + 12*x^3 + 390*x^4 + 18304*x^5 + 1071862*x^6 +...

%e A(A(x)) = x + 2*x^2 + 26*x^3 + 841*x^4 + 39440*x^5 + 2308752*x^6 +...

%e A(A(A(x))) = x + 3*x^2 + 42*x^3 + 1359*x^4 + 63730*x^5 + 3730610*x^6 +...

%e A(A(A(A(x)))) = x + 4*x^2 + 60*x^3 + 1950*x^4 + 91520*x^5 + 5359310*x^6 +...

%e so that 5*A(x) = A(A(A(A(x)))) + 4*x + x^2.

%o (PARI) {a(n)=local(A=x+x^2,G);if(n<1,0,for(i=3,n+1,G=x; for(j=1,4,G=subst(A,x,G+x*O(x^i)));A=A+polcoeff(G,i)*x^i);polcoeff(A,n))}

%Y Cf. A138739, A138913, A138915, A138916.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Apr 03 2008