a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k-1)*4^(n-k-1).

Terms

a(0) =0a(1) =0a(2) =1a(3) =4a(4) =24a(5) =112a(6) =560a(7) =2688a(8) =13056a(9) =62976a(10) =304384a(11) =1469440a(12) =7096320a(13) =34263040a(14) =165441536a(15) =798818304a(16) =3857055744a(17) =18623496192a(18) =89922273280a(19) =434183077888