A112125 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (12th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,12}, with B(0) = 0.

1, 1, -10, 160, -3061, 63775, -1381434, 30233546, -654989371, 13821523157, -280493565375, 5432981693533, -100769609590332, 1833421110751790, -34286913831217395, 678578947805323394, -13377225136748683778, 221000164094797572734, -2119677884300620846621

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...
where A(A(A(A(A(A(A(A(A(A(A(A(x)))))))))))) =
x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 + 12*x^7 + 2*x^8 +...
is the g.f. of A112124.
		

Crossrefs

Cf. A112124, A112104-A112123, A112126, A112127.

Programs

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); return(polcoeff(F,n,x)))}