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A350009 a(n) is the number of isotopism classes containing symmetric Latin squares of order n.

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%I A350009 #19 Dec 08 2021 16:27:28
%S A350009 1,1,1,2,1,6,7,415,3460,35878418,6320290037,4612965997149292,
%T A350009 15859695832489637513
%N A350009 a(n) is the number of isotopism classes containing symmetric Latin squares of order n.
%C A350009 Isotopism classes are obtained by permuting rows, permuting columns and permuting symbols. There is a stronger notion of equivalence called "species" (also known as main classes and paratopism classes). For this particular problem the counts for species equal the counts for isotopism classes.
%H A350009 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 A350009 The odd terms agree with A350010. Cf. A035481
%K A350009 nonn,more
%O A350009 1,4
%A A350009 _Ian Wanless_, Dec 08 2021