A112115 G.f. A(x) satisfies A(A(A(..(A(x))..))) = B(x) (7th self-COMPOSE of A) such that the coefficients of B(x) consist only of numbers {1,2,3,..,7}, with B(0) = 0.

1, 1, -5, 43, -443, 4957, -57281, 661375, -7430526, 79197417, -778914398, 6845802239, -52074744048, 345158019601, -2374391391323, 20218882229451, -34682204747638, -6385759551091470, 180067413599721613, -2110513020510554883

Offset

1,3

Links

Table of n, a(n) for n=1..20.

Example

A(x) = x + x^2 - 5*x^3 + 43*x^4 - 443*x^5 + 4957*x^6 - 57281*x^7 +...
where A(A(A(A(A(A(A(x))))))) =
x + 7*x^2 + 7*x^3 + 7*x^4 + 7*x^5 + 7*x^6 + 7*x^7 +...
is the g.f. of A112114.

Prog

(PARI) {a(n, m=7)=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. A112114, A112104-A112113, A112116-A112127.

Sequence in context: A322246 A306080 A156886 * A350117 A239265 A369023

Adjacent sequences: A112112 A112113 A112114 * A112116 A112117 A112118

Keyword

sign

Author

Paul D. Hanna, Aug 27 2005

Status

approved