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%I #68 Dec 12 2020 06:31:38
%S 1,1,3,18,160,2325,41895,961772,26978400,929587995
%N Maximum determinant of an n X n Latin square.
%C a(n) = A301371(n) for n <= 7. a(8) < A301371(8) = 27296640, a(9) < A301371(9) = 933251220.
%C a(10) = 36843728625, conjectured. See Stack Exchange link. - _Hugo Pfoertner_, Sep 29 2019
%C A328030(n) <= a(n) <= A301371(n). - _Hugo Pfoertner_, Dec 02 2019
%C It is unknown, but very likely, that A301371(n) > a(n) also holds for all n > 9 - _Hugo Pfoertner_, Dec 12 2020
%H Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/latin.html">Latin squares</a>.
%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/885481/maximum-determinant-of-latin-squares">Maximum determinant of Latin squares</a>, (2014), (2016).
%e An example of an 8 X 8 Latin square with maximum determinant is
%e [7 1 3 4 8 2 5 6]
%e [1 7 4 3 6 5 2 8]
%e [3 4 1 7 2 6 8 5]
%e [4 3 7 1 5 8 6 2]
%e [8 6 2 5 4 7 1 3]
%e [2 5 6 8 7 3 4 1]
%e [5 2 8 6 1 4 3 7]
%e [6 8 5 2 3 1 7 4].
%e An example of a 9 X 9 Latin square with maximum determinant is
%e [9 4 3 8 1 5 2 6 7]
%e [3 9 8 5 4 6 1 7 2]
%e [4 1 9 3 2 8 7 5 6]
%e [1 2 4 9 7 3 6 8 5]
%e [8 3 5 6 9 7 4 2 1]
%e [2 7 1 4 6 9 5 3 8]
%e [5 8 6 7 3 2 9 1 4]
%e [7 6 2 1 5 4 8 9 3]
%e [6 5 7 2 8 1 3 4 9].
%e An example of a 10 X 10 Latin square with abs(determinant) = 36843728625 is a circulant matrix with first row [1, 3, 7, 9, 8, 6, 5, 4, 2, 10], but it is not known if this is the best possible. - _Kebbaj Mohamed Reda_, Nov 27 2019 (reworded by _Hugo Pfoertner_)
%Y Cf. A040082, A301371, A308853, A309258, A309984, A328029, A328030.
%K nonn,hard,more
%O 0,3
%A _Hugo Pfoertner_, Aug 26 2019
%E a(9) from _Hugo Pfoertner_, Aug 30 2019
%E a(0)=1 prepended by _Alois P. Heinz_, Oct 02 2019
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