a(n) = n!*b(n) where b(n) = (n-4)*b(n-2)/(n*(n-1)) and b(0) = b(1) = 1.

Terms

a(0) =1a(1) =1a(2) =-2a(3) =-1a(4) =0a(5) =-1a(6) =0a(7) =-3a(8) =0a(9) =-15a(10) =0a(11) =-105a(12) =0a(13) =-945a(14) =0a(15) =-10395a(16) =0a(17) =-135135a(18) =0a(19) =-2027025a(20) =0a(21) =-34459425a(22) =0a(23) =-654729075a(24) =0a(25) =-13749310575a(26) =0a(27) =-316234143225a(28) =0a(30) =0