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

Terms

a(0) =1a(1) =1a(2) =-1a(3) =-2a(4) =13a(5) =-29a(6) =-80a(7) =1268a(8) =-7351a(9) =13276a(10) =245746a(11) =-3632793a(12) =27451743a(13) =-63909390a(14) =-1752952501a(15) =34899085656a(16) =-370619158447