a(n) = Sum_{k = 0..n} (-1)^k*binomial(k,2)^3*binomial(n,k)^3.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =-1296a(5) =0a(6) =303750a(7) =0a(8) =-36879360a(9) =0a(10) =3157481250a(11) =0a(12) =-217564322976a(13) =0a(15) =0a(17) =0a(19) =0a(21) =0a(23) =0a(25) =0