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%I #20 Jun 22 2019 18:58:30
%S 1,3,8,38,192,1320,10176,91296,908160,9985920,119761920,1556847360,
%T 21794734080,326920043520,5230700052480,88921882828800,
%U 1600593472880640,30411275613143040,608225502973132800,12772735554075033600
%N Number of tone-rows in n-tone music.
%H Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 08 2006, <a href="/A099030/b099030.txt">Table of n, a(n) for n = 3..38</a>
%H Samuel Herman, Eirini Poimenidou, <a href="https://arxiv.org/abs/1905.04785">Orbits of Hamiltonian Paths and Cycles in Complete Graphs</a>, arXiv:1905.04785 [math.CO], 2019.
%H H. Fripertinger, <a href="http://www.mat.univie.ac.at/~slc/opapers/s26fripert.html">Enumeration in musical theory</a>, Séminaire Lotharingien de Combinatoire, B26a (1991), 14 pp.
%F (1/4) [(n-1)!+(n-1)!! ] if n odd, (1/4) [(n-1)!+(n/2+1)(n-2)!! ] if even.
%t a[n_] := If[OddQ[n], (n-1)! + (n-1)!!, (n-1)! + (n/2 + 1)*(n-2)!!] / 4;
%t Table[a[n], {n, 3, 38}] (* _Jean-François Alcover_, Aug 01 2016 *)
%o (PARI) doubfact(n)=if(n<2, 1, n*doubfact(n-2));
%o for(n=3,50,if(n%2==1,print1(((n-1)!+doubfact(n-1))/4,","),print1(((n-1)!+(n/2+1)*doubfact(n-2))/4,","))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 02 2006
%Y Apart from initial terms, same as A089066. - _Ray Jerome_, Feb 25 2005
%K nonn,easy
%O 3,2
%A _Ralf Stephan_, Sep 27 2004
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 02 2006
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