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A112115 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (7th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,7}, with B(0) = 0.

%I A112115 #6 Mar 12 2015 22:20:28
%S A112115 1,1,-5,43,-443,4957,-57281,661375,-7430526,79197417,-778914398,
%T A112115 6845802239,-52074744048,345158019601,-2374391391323,20218882229451,
%U A112115 -34682204747638,-6385759551091470,180067413599721613,-2110513020510554883
%N A112115 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (7th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,7}, with B(0) = 0.
%e A112115 A(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 +...
%e A112115 where A(A(A(A(A(A(A(x))))))) =
%e A112115 x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 +...
%e A112115 is the g.f. of A112114.
%o A112115 (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); return(polcoeff(F,n,x)))}
%Y A112115 Cf. A112114, A112104-A112113, A112116-A112127.
%K A112115 sign
%O A112115 1,3
%A A112115 _Paul D. Hanna_, Aug 27 2005