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

Terms

a(0) =1a(1) =1a(2) =-1a(3) =-5a(4) =5a(5) =56a(6) =-29a(7) =-923a(8) =-119a(9) =19855a(10) =17711a(11) =-524160a(12) =-926771a(13) =16339441a(14) =45275035a(15) =-585443909a(16) =-2298643951a(17) =23626165600a(18) =124604211943