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a(n) is the number of equivalence classes of symmetric Latin squares of order n.
3

%I #20 Dec 08 2021 16:28:11

%S 1,1,1,2,1,6,7,423,3460,35878510,6320290037,4612966007179768,

%T 15859695832489637513

%N a(n) is the number of equivalence classes of symmetric Latin squares of order n.

%C Equivalence here includes permutation of the symbols as well as simultaneously applying one permutation to both the rows and columns.

%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 The odd terms agree with A350009. Cf. A035481.

%K nonn,more

%O 1,4

%A _Ian Wanless_, Dec 08 2021