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%I #10 Oct 08 2018 18:34:52
%S 1,7,7,7,7,7,7,7,6,6,6,6,6,6,5,3,3,3,3,3,2,2,1,1,1,1,7,4,7,4,4,4,3,2,
%T 5,3,1,1,7,5,2,4,2,2,1,2,6,5,1,5,7,7,7,7,5,6,5,6,4,1,6,1,2,7,1,5,3,7,
%U 2,4,4,4,3,2,4,5,7,7,3,1,2,3,5,5,6,4,7,6,1,6,5,2,1,1,6,1,4,3,1,2,3,3,3,7,1
%N Unique sequence of numbers {1,2,3,...,7} where g.f. A(x) satisfies A(x) = B(B(B(..(B(x))..))) (7th self-COMPOSE) such that B(x) is an integer series, with A(0) = 0.
%e G.f.: A(x) = x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 + ...
%e then A(x) = B(B(B(B(B(B(B(x))))))) where
%e B(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 + ...
%e is the g.f. of A112115.
%o (PARI) {a(n,m=7)=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. A112115, A112104-A112113, A112116-A112127.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Aug 27 2005
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