editing

approved

G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (12-th 12th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,12}, with B(0) = 0.

approved

editing

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Aug 27 2005

sign,new

sign

Paul D . Hanna (pauldhanna(AT)juno.com), Aug 27 2005

1,43

(PARI) {a(n, m=12)=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)))}

sign,new

sign

G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (12-th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,12}, with B(0) = 0.

1, 1, -10, 160, -3061, 63775, -1381434, 30233546, -654989371, 13821523157, -280493565375, 5432981693533, -100769609590332, 1833421110751790, -34286913831217395, 678578947805323394, -13377225136748683778, 221000164094797572734, -2119677884300620846621

1,4

A(x) = x + x^2 - 10*x^3 + 160*x^4 - 3061*x^5 + 63775*x^6 +...

where A(A(A(A(A(A(A(A(A(A(A(A(x)))))))))))) =

x + 12*x^2 + 12*x^3 + 6*x^4 + 8*x^5 + 8*x^6 + 12*x^7 + 2*x^8 +...

is the g.f. of A112124.

(PARI) {a(n, m=12)=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)))}

Cf. A112124, A112104-A112123, A112126, A112127.

sign

Paul D Hanna (pauldhanna(AT)juno.com), Aug 27 2005

approved