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.

1, 1, -5, 43, -443, 4957, -57281, 661375, -7430526, 79197417, -778914398, 6845802239, -52074744048, 345158019601, -2374391391323, 20218882229451, -34682204747638, -6385759551091470, 180067413599721613, -2110513020510554883

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 +...
where A(A(A(A(A(A(A(x))))))) =
x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 +...
is the g.f. of A112114.
		

Crossrefs

Cf. A112114, A112104-A112113, A112116-A112127.

Programs

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)))}