a(n) = binomial(n - 1, ceiling(n/2)) * binomial(n - 1, ceiling(n/2) - 1).

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =9a(5) =24a(6) =100a(7) =300a(8) =1225a(9) =3920a(10) =15876a(11) =52920a(12) =213444a(13) =731808a(14) =2944656a(15) =10306296a(16) =41409225a(17) =147232800a(18) =590976100a(19) =2127513960a(20) =8533694884a(21) =31031617760a(22) =124408576656a(23) =456164781072