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

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =-2a(5) =-4a(6) =-1a(7) =14a(8) =34a(9) =2a(10) =-189a(11) =-439a(12) =263a(13) =3796a(14) =6997a(15) =-14437a(16) =-96643a(17) =-106774a(18) =671097a(19) =2800836a(20) =57519a(21) =-31088662a(22) =-82674287a(23) =155322877a(24) =1455331563a(25) =1936970102a(26) =-14267868745a(27) =-66446614533a(28) =19215003803