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%I #8 Mar 31 2012 20:25:00
%S 1,0,0,48,1440,0,19353600,4180377600,25070769561600,
%T 3200285563453440000
%N Number of self-orthogonal Latin squares of order n.
%C A self-orthogonal Latin square is a Latin square orthogonal to its transpose and a SOLS L is idempotent if L(i,i)=i. The number of distinct SOLS of order n may be determined by multiplying the number of idempotent SOLS of order n by n!.
%D G. P. Graham and C.E. Roberts, 2006. Enumeration and isomorphic classification of self-orthogonal Latin squares, Journal of Combinatorial Mathematics and Combinatorial Computing, 59, pp. 101-118.
%H A. P. Burger, M. P. Kidd and J. H. van Vuuren, 2010. <a href="http://www.vuuren.co.za/papers/SOLSEnum10.pdf">Enumerasie van self-ortogonale Latynse vierkante van orde 10</a>, LitNet Akademies (Natuurwetenskappe), 7(3), pp 1-22.
%H A. P. Burger, M. P. Kidd and J. H. van Vuuren, <a href="http://www.vuuren.co.za/papers/SOLSEnum.pdf">Enumeration of isomorphism classes of self-orthogonal Latin squares</a>, Ars Combinatoria, 97, pp. 143-152.
%H M. P. Kidd, <a href="http://www.vuuren.co.za/main.php">A repository of self-orthogonal Latin squares</a>
%Y Cf. A160365, A160366, n!*A160367.
%K hard,more,nonn
%O 1,4
%A _Martin P Kidd_, May 11 2009
%E References updated and a link updated by _Martin P Kidd_, Aug 14 2010
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