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A112117 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (8th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,8}, with B(0) = 0.

%I A112117 #6 Mar 12 2015 19:57:38
%S A112117 1,1,-6,60,-720,9398,-126958,1719439,-22778647,288721672,-3426131120,
%T A112117 37291873546,-368633930696,3421668183648,-33763691015949,
%U A112117 382711017377914,-3403489111329505,-22613095886515578,1672401759052466166,-27936127591842262118,-15637150116164531317
%N A112117 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (8th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,8}, with B(0) = 0.
%e A112117 A(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 +...
%e A112117 where A(A(A(A(A(A(A(A(x)))))))) =
%e A112117 x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
%e A112117 is the g.f. of A112116.
%o A112117 (PARI) {a(n,m=8)=local(F=x+x^2+x*O(x^n),G);if(n<1,0, for(k=3,n, G=F+x*O(x^k);for(i=1,m-1,G=subst(F,x,G)); F=F-((polcoeff(G,k)-1)\m)*x^k); return(polcoeff(F,n,x)))}
%Y A112117 Cf. A112116, A112104-A112115, A112118-A112127.
%K A112117 sign
%O A112117 1,3
%A A112117 _Paul D. Hanna_, Aug 27 2005