a(n) = Sum_{k=0..floor(3*n/5)} binomial(k+2,2) * binomial(k,3*n-5*k).

Terms

a(0) =1a(1) =0a(2) =3a(3) =0a(4) =6a(5) =10a(6) =10a(7) =60a(8) =15a(9) =210a(10) =49a(11) =560a(12) =280a(13) =1260a(14) =1296a(15) =2575a(16) =4665a(17) =5280a(18) =13915a(19) =12210a(20) =36193a(21) =32890a(22) =85527a(23) =95095a(24) =191191a(25) =270406a(26) =422345a(27) =726808a(28) =959260a(29) =1835456