A112107 G.f. A(x) satisfies A(A(A(x))) = B(x) (3rd self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3}, with B(0) = 0.

1, 1, -1, 3, -10, 35, -119, 360, -792, -33, 12779, -82525, 305861, -552011, -126321, -8385020, 138177591, -433073834, -5366414982, 51203452090, 123835509276, -4174647911014, 5274854624423, 373574363131841, -2054088594386738, -34047892948849106, 391005463740951942

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - x^3 + 3*x^4 - 10*x^5 + 35*x^6 - 119*x^7 + ...
where A(A(A(x))) = x + 3*x^2 + 3*x^3 + 3*x^4 + 2*x^5 + ...
is the g.f. of A112106.
		

Crossrefs

Cf. A112106, A112104, A112105, A112108-A112127.

Programs

PARI

{a(n,m=3)=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)))}