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%I #7 Feb 19 2021 20:10:00
%S 1,2,21,402,13805,761154,62523664,7237970648,1132600004910,
%T 231900134422880,60528794385067778,19713593779259862624,
%U 7869483395065035685162,3792402572391137423764584
%N Number of orbits of length n under the map whose periodic points are counted by A061684.
%C Old name was: A061684 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.
%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 in A061684, then a(n) = (1/n)*Sum_{d|n}mu(d)b(n/d).
%e The sequence A061684 begins 1,1,5,64,1613, so a(3)=(b(3)-b(1))/3=21.
%Y Cf. A061684.
%K nonn
%O 1,2
%A _Thomas Ward_, Feb 24 2004
%E Name clarified by _Michel Marcus_, May 14 2015
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