a(n) = 3^(n-1) + C(2*n, n)/2.

Terms

a(0) =2a(1) =6a(2) =19a(3) =62a(4) =207a(5) =705a(6) =2445a(7) =8622a(8) =30871a(9) =112061a(10) =411765a(11) =1529225a(12) =5731741a(13) =21652623a(14) =82341729a(15) =314889102a(16) =1209849831a(17) =4666707813a(18) =18060052389a(19) =70085525877a(20) =272615721621