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%I #6 Mar 12 2015 19:57:38
%S 1,1,-6,60,-720,9398,-126958,1719439,-22778647,288721672,-3426131120,
%T 37291873546,-368633930696,3421668183648,-33763691015949,
%U 382711017377914,-3403489111329505,-22613095886515578,1672401759052466166,-27936127591842262118,-15637150116164531317
%N 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 A(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 +...
%e where A(A(A(A(A(A(A(A(x)))))))) =
%e x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
%e is the g.f. of A112116.
%o (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 Cf. A112116, A112104-A112115, A112118-A112127.
%K sign
%O 1,3
%A _Paul D. Hanna_, Aug 27 2005
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