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A112120 Unique sequence of numbers {1,2,3,...,10} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (10th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

%I A112120 #6 Mar 14 2015 01:08:55
%S A112120 1,10,10,5,10,5,8,3,4,3,2,1,9,2,8,1,7,4,9,4,7,8,2,4,5,5,6,5,6,6,6,5,6,
%T A112120 7,3,1,2,10,10,10,5,7,10,1,4,7,1,1,5,7,2,8,9,4,3,7,5,10,4,4,9,8,7,8,4,
%U A112120 6,7,1,2,2,3,5,9,1,10,2,5,4,5,9,3,4,10,1,1,10,4,2,6,4,8,2,2,4,9,2,10,8,4,7
%N A112120 Unique sequence of numbers {1,2,3,...,10} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (10th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
%e A112120 G.f.: A(x) = x + 10*x^2 + 10*x^3 + 5*x^4 + 10*x^5 + 5*x^6 +...
%e A112120 then A(x) = B(B(B(B(B(B(B(B(B(B(x)))))))))) where
%e A112120 B(x) = x + x^2 - 8*x^3 + 104*x^4 - 1619*x^5 + 27437*x^6 +...
%e A112120 is the g.f. of A112121.
%o A112120 (PARI) {a(n,m=10)=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 A112120 Cf. A112121, A112104-A112119, A112122-A112127.
%K A112120 nonn
%O A112120 1,2
%A A112120 _Paul D. Hanna_, Aug 27 2005