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A138916 G.f. A(x) satisfies: 7*A(x) = A(A(A(A(A(A(x)))))) + 6*x + x^2 with A(0)=0.

%I A138916 #4 Mar 12 2015 23:38:35
%S A138916 1,1,30,2385,273560,39078970,6512700536,1222156339336,252751878117712,
%T A138916 56798072762849412,13733835430565197700,3548014267149570778764,
%U A138916 974073193845291808779496,283008950620416071533339000
%N A138916 G.f. A(x) satisfies: 7*A(x) = A(A(A(A(A(A(x)))))) + 6*x + x^2 with A(0)=0.
%C A138916 A(A(A(A(A(A(x)))))) is the 6th self-composition of the g.f. A(x).
%e A138916 G.f.: A(x) = x + x^2 + 30*x^3 + 2385*x^4 + 273560*x^5 +...
%e A138916 A(A(x)) = x + 2*x^2 + 62*x^3 + 4921*x^4 + 564280*x^5 +...
%e A138916 A(A(A(x))) = x + 3*x^2 + 96*x^3 + 7614*x^4 + 872950*x^5 +...
%e A138916 A(A(A(A(x)))) = x + 4*x^2 + 132*x^3 + 10470*x^4 + 1200384*x^5 +...
%e A138916 A(A(A(A(A(x))))) = x + 5*x^2 + 170*x^3 + 13495*x^4 + 1547420*x^5 +...
%e A138916 A(A(A(A(A(A(x)))))) = x + 6*x^2 + 210*x^3 + 16695*x^4 + 1914920*x^5 +...
%e A138916 so that 7*A(x) = A(A(A(A(A(A(x)))))) + 6*x + x^2.
%o A138916 (PARI) {a(n)=local(A=x+x^2,G);if(n<1,0,for(i=3,n+1,G=x; for(j=1,6,G=subst(A,x,G+x*O(x^i)));A=A+polcoeff(G,i)*x^i);polcoeff(A,n))}
%Y A138916 Cf. A138739, A138913, A138914, A138915.
%K A138916 nonn
%O A138916 1,3
%A A138916 _Paul D. Hanna_, Apr 03 2008