On the enumeration of self-complementary m-placed relations

A formula for the number a_m(2n) of self-complementary m-placed relations is given. Then we obtain from this formula asymptotic results, e.g.$\text{a}{}_{\mathrm{m}}\text{(2n) ～ (2(}{}^{\mathrm{2n}}\text{)}{}^{\mathrm{<mtext>m</mtext><mtext>2?n</mtext>}}\text{)/n}$