a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(3*k,n-2*k).

Terms

a(0) =1a(1) =0a(2) =2a(3) =9a(4) =22a(5) =95a(6) =371a(7) =1316a(8) =5190a(9) =20070a(10) =76967a(11) =301301a(12) =1177267a(13) =4607512a(14) =18128196a(15) =71413124a(16) =281868534a(17) =1115006013a(18) =4416906098a(19) =17522237304a(20) =69606918227a(21) =276828568445