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A138914 G.f. A(x) satisfies: 5*A(x) = A(A(A(A(x)))) + 4*x + x^2 with A(0)=0.

%I A138914 #4 Mar 14 2015 10:13:17
%S A138914 1,1,12,390,18304,1071862,73349996,5661162666,482252816998,
%T A138914 44704184452202,4465265748489708,477159108766899654,
%U A138914 54255973609630750372,6536766146592886952548,831617552461457925554152
%N A138914 G.f. A(x) satisfies: 5*A(x) = A(A(A(A(x)))) + 4*x + x^2 with A(0)=0.
%C A138914 A(A(A(A(x)))) is the 4th self-composition of the g.f. A(x).
%e A138914 G.f.: A(x) = x + x^2 + 12*x^3 + 390*x^4 + 18304*x^5 + 1071862*x^6 +...
%e A138914 A(A(x)) = x + 2*x^2 + 26*x^3 + 841*x^4 + 39440*x^5 + 2308752*x^6 +...
%e A138914 A(A(A(x))) = x + 3*x^2 + 42*x^3 + 1359*x^4 + 63730*x^5 + 3730610*x^6 +...
%e A138914 A(A(A(A(x)))) = x + 4*x^2 + 60*x^3 + 1950*x^4 + 91520*x^5 + 5359310*x^6 +...
%e A138914 so that 5*A(x) = A(A(A(A(x)))) + 4*x + x^2.
%o A138914 (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 A138914 Cf. A138739, A138913, A138915, A138916.
%K A138914 nonn
%O A138914 1,3
%A A138914 _Paul D. Hanna_, Apr 03 2008