a(n) = Sum_{i=1..n-1} (-1)^i*binomial(n, i-1)*binomial(n, i)*binomial(n, i+1).

Terms

a(0) =0a(1) =-2a(2) =0a(3) =48a(4) =0a(5) =-1080a(6) =0a(7) =24640a(8) =0a(9) =-573300a(10) =0a(11) =13571712a(12) =0a(13) =-325909584a(14) =0a(15) =7918859520a(16) =0a(17) =-194292083700a(18) =0a(20) =0a(22) =0a(24) =0a(26) =0a(28) =0