%N Number of n X n symmetric matrices each of whose rows is a permutation of 1..n.
%C The even and odd subsequences are A036980, A036981.
%F a(n) = A035481(n) * n!. [From _Max Alekseyev_, Apr 23 2010]
%e a(3) = 6 because the first row is arbitrary (say, 213) and the rest is then determined. By symmetry the second row has to be 132 or 123 but in order for the third row/column to work it has to be 132.
%Y Cf. A000438, A035481, A000315, A002860, A003090, A040082.
%A _Joshua Zucker_ and Joe Keane