a(n) = (1 + Sum_{j=0..n} (C(n,j)*C(3*j-1,j))) / 2.

Terms

a(0) =1a(1) =2a(2) =8a(3) =47a(4) =312a(5) =2162a(6) =15311a(7) =109965a(8) =797824a(9) =5833298a(10) =42910998a(11) =317224800a(12) =2354712927a(13) =17538747124a(14) =131017428431a(15) =981194304302