a(n) = 4*C(2n,n) - 3*0^n.

Terms

a(0) =1a(1) =8a(2) =24a(3) =80a(4) =280a(5) =1008a(6) =3696a(7) =13728a(8) =51480a(9) =194480a(10) =739024a(11) =2821728a(12) =10816624a(13) =41602400a(14) =160466400a(15) =620470080a(16) =2404321560a(17) =9334424880a(18) =36300541200a(19) =141381055200a(20) =551386115280