OFFSET
1,2
COMMENTS
Old name was: A061687 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n for that map.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..100
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
Thomas Ward, Exactly realizable sequences. [local copy].
FORMULA
If b(n) is the (n+1)th term of A061687, then a(n) = (1/n)*Sum_{d|n} mu(d)*b(n/d).
EXAMPLE
b(1)=1, b(3)=8506, so a(3) = (1/3)*(8506-1) = 2835.
MAPLE
with(numtheory):
b:= proc(n) option remember;
`if`(n=0, 1, add(binomial(n, k)^6*(n-k)*b(k)/n, k=0..n-1))
end:
a:= n-> add(mobius(d)*b(n/d), d=divisors(n))/n:
seq(a(n), n=1..15); # Alois P. Heinz, Mar 19 2014
MATHEMATICA
b[n_] := b[n] = If[n==0, 1, Sum[Binomial[n, k]^6 (n-k)b[k]/n, {k, 0, n-1}]];
a[n_] := Sum[MoebiusMu[d] b[n/d], {d, Divisors[n]}]/n;
Array[a, 15] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ward, Feb 24 2004
EXTENSIONS
More terms from Alois P. Heinz, Mar 19 2014
Name clarified by Michel Marcus, May 13 2015
STATUS
approved