%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