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

Terms

a(0) =0a(1) =1a(2) =-3a(3) =-8a(4) =45a(5) =126a(6) =-840a(7) =-2400a(8) =17325a(9) =50050a(10) =-378378a(11) =-1100736a(12) =8576568a(13) =25069968a(14) =-199536480a(15) =-585307008a(16) =4732755885a(17) =13919870250a(18) =-113936715750a(19) =-335813478000