a(n) = 3*binomial(2*n+1,n+1) - n^2 - 2*n - 4.

Terms

a(0) =2a(1) =18a(2) =86a(3) =350a(4) =1347a(5) =5096a(6) =19238a(7) =72846a(8) =277031a(9) =1058024a(10) =4056087a(11) =15600728a(12) =60174701a(13) =232676052a(14) =901620326a(15) =3500409038a(16) =13612702623a(17) =53017895336a(18) =206769792827a(19) =807386811216