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A091160
Number of orbits of length n under the map whose periodic points are counted by A061687.
1
1, 16, 2835, 2370752, 6611343125, 48887897438124, 821067869874486556, 28006755051982013513984, 1782755223314276717178818904, 198173677662343700104263938337400, 36467946245662764068249155883368682252, 10631160782054640951386529213624176084501136
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
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.
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
Cf. A061687.
Sequence in context: A221253 A374414 A123282 * A049030 A223068 A051551
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