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%I #19 Nov 15 2017 02:57:49
%S 1,0,1,2,18,0,342480,7850589120,7188534981260640
%N Number of reduced pairs of orthogonal Latin squares.
%C A pair of orthogonal Latin squares is reduced if their first rows are in natural order and so is the first column of the first square.
%H J. Egan and I. M. Wanless, <a href="http://dx.doi.org/10.1090/mcom/3010">Enumeration of MOLS of small order</a>, Mathematics of Computation 85, 2016, 799-824.
%H Stepan Kochemazov, Oleg Zaikin, Alexander Semenov, <a href="https://dx.doi.org/10.23919/MIPRO.2017.7973600">Runtime Estimation for Enumerating all Mutually Orthogonal Diagonal Latin Squares of Order 10</a>, 2017 40th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO). <a href="http://docs.mipro-proceedings.com/cis/cis_18_4252.pdf">PDF download</a>
%H Ian Wanless, <a href="http://users.monash.edu.au/~iwanless/data/MOLS/">Data on MOLS</a>
%Y Sequence A072377 is obtained from this sequence by multiplying by n!n!(n-1)!/2 (except when n=1).
%K nonn,nice,more
%O 1,4
%A _Ian Wanless_, Dec 22 2015
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