%I #6 Mar 11 2020 18:05:32
%S 1,2,3,4,6,8,17,36,146,1066,15419,406684,19284912,1635874946,
%T 249424764407,68725494158824,34418706513939926,31487353344361957012,
%U 52887877379630894268187,163777247316556715401451972,939121048579630147375554814224
%N Number of non-isomorphic n X n symmetric binary matrices with an equal number of ones in every row and column up to permutation of rows and columns.
%C a(n) is the number of regular bicolored graphs on 2n unlabeled nodes which are invariant when the two color classes are interchanged.
%e The a(2) = 3 matrices are:
%e [0 0] [1 0] [1 1]
%e [0 0] [0 1] [1 1]
%Y Row sums of A333159.
%Y Cf. A122082, A322698, A333162.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Mar 10 2020