A112127 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (13th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,13}, with B(0) = 0.

1, 1, -11, 193, -4043, 92233, -2188907, 52544305, -1250612651, 29060631481, -651497950667, 13997025548641, -289196932607819, 5873067677083177, -122109541297984368, 2669034419647762122, -58550172867811577842, 1127335101086707607932

Offset: 1

Author

Paul D. Hanna, Aug 27 2005

Keywords

• sign

Examples

			A(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...
where A(A(A(A(A(A(A(A(A(A(A(A(A(x))))))))))))) =
x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 + 13*x^7 +...
is the g.f. of A112126.
		

Crossrefs

Cf. A112126, A112104-A112125.

Programs

PARI

{a(n,m=13)=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)))}