A112127 - OEIS

%I #6 Mar 14 2015 00:05:40

%S 1,1,-11,193,-4043,92233,-2188907,52544305,-1250612651,29060631481,

%T -651497950667,13997025548641,-289196932607819,5873067677083177,

%U -122109541297984368,2669034419647762122,-58550172867811577842,1127335101086707607932

%N 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.

%e A(x) = x + x^2 - 11*x^3 + 193*x^4 - 4043*x^5 + 92233*x^6 +...

%e where A(A(A(A(A(A(A(A(A(A(A(A(A(x))))))))))))) =

%e x + 13*x^2 + 13*x^3 + 13*x^4 + 13*x^5 + 13*x^6 + 13*x^7 +...

%e is the g.f. of A112126.

%o (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)))}

%Y Cf. A112126, A112104-A112125.

%K sign

%O 1,3

%A _Paul D. Hanna_, Aug 27 2005