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%I #6 Mar 12 2015 18:41:39
%S 1,9,9,9,6,6,3,9,6,3,9,3,3,1,7,5,9,1,8,6,2,6,4,6,7,6,4,6,3,2,5,7,2,5,
%T 7,8,1,4,9,6,3,7,6,9,1,7,7,3,7,8,7,5,7,8,9,3,8,7,9,5,3,9,9,1,5,4,5,1,
%U 7,3,1,7,8,6,1,8,4,6,8,6,5,5,9,2,6,1,5,9,8,7,2,8,8,3,2,3,9,8,2,8,4,6,1,9,4
%N Unique sequence of numbers {1,2,3,...,9} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (9th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
%e G.f.: A(x) = x + 9*x^2 + 9*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 +...
%e then A(x) = B(B(B(B(B(B(B(B(B(x))))))))) where
%e B(x) = x + x^2 - 7*x^3 + 81*x^4 - 1122*x^5 + 16906*x^6 +...
%e is the g.f. of A112119.
%o (PARI) {a(n,m=9)=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); G=F+x*O(x^n);for(i=1,m-1,G=subst(F,x,G)); return(polcoeff(G,n,x)))}
%Y Cf. A112119, A112104-A112117, A112120-A112127.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 27 2005
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