A112117 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (8th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,8}, with B(0) = 0.

1, 1, -6, 60, -720, 9398, -126958, 1719439, -22778647, 288721672, -3426131120, 37291873546, -368633930696, 3421668183648, -33763691015949, 382711017377914, -3403489111329505, -22613095886515578, 1672401759052466166, -27936127591842262118, -15637150116164531317

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 +...
where A(A(A(A(A(A(A(A(x)))))))) =
x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
is the g.f. of A112116.
		

Crossrefs

Cf. A112116, A112104-A112115, A112118-A112127.

Programs

PARI

{a(n,m=8)=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)))}