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

Terms

a(0) =0a(1) =1a(2) =-1a(3) =-8a(4) =15a(5) =126a(6) =-280a(7) =-2400a(8) =5775a(9) =50050a(10) =-126126a(11) =-1100736a(12) =2858856a(13) =25069968a(14) =-66512160a(15) =-585307008a(16) =1577585295a(17) =13919870250a(18) =-37978905250a(19) =-335813478000a(20) =925166131890