a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-2*k-3,n-2*k).

Terms

a(0) =1a(1) =-1a(2) =-1a(3) =0a(4) =3a(5) =14a(6) =58a(7) =234a(8) =931a(9) =3674a(10) =14434a(11) =56576a(12) =221518a(13) =867008a(14) =3393544a(15) =13286350a(16) =52040483a(17) =203936538a(18) =799621994a(19) =3137022800a(20) =12313867738a(21) =48362815668a(22) =190047775804a(23) =747206147380