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A112124 Unique sequence of numbers {1,2,3,...,12} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (12th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.

%I A112124 #6 Mar 13 2015 23:48:05
%S A112124 1,12,12,6,8,8,12,2,8,2,10,9,10,10,4,5,4,7,10,10,12,7,12,8,8,9,10,7,
%T A112124 11,12,2,9,12,10,11,7,6,5,4,5,10,7,9,1,9,5,12,12,2,10,6,9,9,6,2,1,9,3,
%U A112124 7,10,4,11,10,3,6,10,6,10,12,11,8,1,2,4,7,2,8,6,9,12,8,2,3,2,4,3,6,12,6,11,4
%N A112124 Unique sequence of numbers {1,2,3,...,12} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (12th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
%e A112124 G.f.: A(x) = x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 +...
%e A112124 then A(x) = B(B(B(B(B(B(B(B(B(B(B(B(x)))))))))))) where
%e A112124 B(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...
%e A112124 is the g.f. of A112125.
%o A112124 (PARI) {a(n,m=12)=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 A112124 Cf. A112125, A112104-A112123, A112126, A112127.
%K A112124 nonn
%O A112124 1,2
%A A112124 _Paul D. Hanna_, Aug 27 2005