A112123 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (11th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,11}, with B(0) = 0.

1, 1, -9, 131, -2279, 43161, -849269, 16866851, -331093879, 6316647841, -115528321709, 2007845708091, -33238536213650, 537616162919975, -8956186512464320, 158920634214746905, -2786226293720310297, 38547971903938600271, -198392033014273765511

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - 9*x^3 + 131*x^4 - 2279*x^5 + 43161*x^6 - 849269*x^7 +...
where A(A(A(A(A(A(A(A(A(A(A(x))))))))))) =
x + 11*x^2 + 11*x^3 + 11*x^4 + 11*x^5 + 11*x^6 + 11*x^7 +...
is the g.f. of A112122.
		

Crossrefs

Cf. A112122, A112104-A112121, A112124-A112127.

Programs

PARI

{a(n,m=11)=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)))}