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Number of totally symmetric Latin squares of order n.
1

%I #20 Dec 02 2022 19:46:10

%S 1,2,3,16,30,480,1290,163200,471240,386400000,2269270080,

%T 12238171545600,149648961369600,8089070513113497600,

%U 160650421233958656000,91361407076595590705971200

%N Number of totally symmetric Latin squares of order n.

%C A Latin square is "totally symmetric" if all 6 of its conjugates are equal.

%H Hy Ginsberg, <a href="https://arxiv.org/abs/2211.13204">Totally Symmetric Quasigroups of Order 16</a>, arXiv preprint (2022). arXiv:2211.13204 [math.CO]

%H Brendan D. McKay and Ian M. Wanless, <a href="https://doi.org/10.1002/jcd.21814">Enumeration of Latin squares with conjugate symmetry</a>, J. Combin. Des. 30 (2022), 105-130.

%Y Cf. A076019, A350026.

%K nonn,more

%O 1,2

%A _Ian Wanless_, Dec 08 2021

%E a(16) from Ginsberg link via _Charles R Greathouse IV_, Dec 02 2022