A112113 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (6th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,6}, with B(0) = 0.

1, 1, -4, 28, -236, 2159, -20309, 189387, -1696165, 14092143, -103605487, 621674576, -2503235595, 1311059747, 58857366823, -625935119621, 20416246154579, -595556154741631, 9331660766550500, -50486760747953952, -816026626910008666

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - 4*x^3 + 28*x^4 - 236*x^5 + 2159*x^6 +...
where A(A(A(A(A(A(x)))))) =
x + 6*x^2 + 6*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 6*x^7 + 2*x^8 +...
is the g.f. of A112112.
		

Crossrefs

Cf. A112112, A112104-A112111, A112114-A112127.

Programs

PARI

{a(n,m=6)=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)))}