A112119 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (9th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,9}, with B(0) = 0.

1, 1, -7, 81, -1122, 16906, -264109, 4150081, -64119406, 955386299, -13491950523, 178108552187, -2193288809125, 25965294143459, -320197330438145, 4331428366450929, -54509980572007649, 309687851858995853, 8841175049606909354, -260481122023484957344, 727627679068983588258

Offset

1,3

Links

Table of n, a(n) for n=1..21.

Example

A(x) = x + x^2 - 7*x^3 + 81*x^4 - 1122*x^5 + 16906*x^6 +...
where A(A(A(A(A(A(A(A(A(x))))))))) =
x + 9*x^2 + 9*x^3 + 9*x^4 + 6*x^5 + 6*x^6 + 3*x^7 +...
is the g.f. of A112118.

Prog

(PARI) {a(n, m=9)=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. A112118, A112104-A112117, A112120-A112127.

Sequence in context: A088735 A364322 A339710 * A369024 A371027 A058575

Adjacent sequences: A112116 A112117 A112118 * A112120 A112121 A112122

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved