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Number of orbits of length n under the map whose periodic points are counted by A061688.
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%I #7 Feb 19 2021 20:10:00

%S 1,32,16281,52293792,692825815625,28927809504181734

%N Number of orbits of length n under the map whose periodic points are counted by A061688.

%C Old name was: A061688 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 under that map.

%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

%H J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

%H Thomas Ward, <a href="http://web.archive.org/web/20081002082625/http://www.mth.uea.ac.uk/~h720/research/files/integersequences.html">Exactly realizable sequences</a>. <a href="/A091112/a091112.pdf">[local copy]</a>.

%F If b(n) is the (n+1)th term of A061688, then a(n) = (1/n)*Sum_{d|n}mu(d)b(n/d).

%e b(1)=1,b(3)=48844, so a(3)=(1/3)(48844-1)=16281.

%Y Cf. A061688.

%K nonn

%O 1,2

%A _Thomas Ward_, Feb 24 2004

%E Name clarified by _Michel Marcus_, May 14 2015