A112125 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (12th 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

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Example

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.

Prog

(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)))}

Crossrefs

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

Sequence in context: A284110 A180881 A106261 * A366037 A090374 A034724

Adjacent sequences: A112122 A112123 A112124 * A112126 A112127 A112128

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved