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%I #30 Mar 12 2022 21:40:50
%S 1,1,1,2,2,17,324,842227,57810418543,104452188344901572,
%T 6108088657705958932053657
%N Number of types of Latin squares of order n. Equivalently, number of nonisomorphic 1-factorizations of K_{n,n}.
%C Here "type" means an equivalence class of Latin squares under the operations of row permutation, column permutation, symbol permutation and transpose. In the 1-factorizations formulation, these operations are labeling of left side, labeling of right side, permuting the order in which the factors are listed and swapping the left and right sides, respectively. - _Brendan McKay_
%C There are 6108088657705958932053657 isomorphism classes of one-factorizations of K_{11,11}. - Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009
%D CRC Handbook of Combinatorial Designs, 1996, p. 660.
%D Denes and Keedwell, Latin Squares and Applications, Academic Press 1974.
%H A. Hulpke, Petteri Kaski and Patric R. J. Östergård, <a href="http://dx.doi.org/10.1090/S0025-5718-2010-02420-2">The number of Latin squares of order 11</a>, Math. Comp. 80 (2011) 1197-1219
%H B. D. McKay, A. Meynert and W. Myrvold, <a href="http://users.cecs.anu.edu.au/~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</a>, J. Combin. Designs, to appear (2005).
%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%Y See A040082 for another version.
%Y Cf. A002860, A003090, A000315, A040082, A000479.
%K hard,nonn,nice,more
%O 1,4
%A _N. J. A. Sloane_
%E More terms from _Richard Bean_, Feb 17 2004
%E a(11) from Petteri Kaski (petteri.kaski(AT)cs.helsinki.fi), Sep 18 2009
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