A112117 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (8th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,8}, with B(0) = 0.

1, 1, -6, 60, -720, 9398, -126958, 1719439, -22778647, 288721672, -3426131120, 37291873546, -368633930696, 3421668183648, -33763691015949, 382711017377914, -3403489111329505, -22613095886515578, 1672401759052466166, -27936127591842262118, -15637150116164531317

Offset

1,3

Links

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

Example

A(x) = x + x^2 - 6*x^3 + 60*x^4 - 720*x^5 + 9398*x^6 +...
where A(A(A(A(A(A(A(A(x)))))))) =
x + 8*x^2 + 8*x^3 + 4*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
is the g.f. of A112116.

Prog

(PARI) {a(n, m=8)=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. A112116, A112104-A112115, A112118-A112127.

Sequence in context: A232246 A086984 A000894 * A065944 A357771 A126779

Adjacent sequences: A112114 A112115 A112116 * A112118 A112119 A112120

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved