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

Terms

a(0) =1a(1) =4a(2) =16a(3) =62a(4) =236a(5) =892a(6) =3368a(7) =12742a(8) =48364a(9) =184244a(10) =704408a(11) =2702108a(12) =10396504a(13) =40108408a(14) =155101136a(15) =601047622a(16) =2333540684a(17) =9075004228a(18) =35345001656a(19) =137846004532a(20) =538256825864