a(n) = binomial(3*n-2,n+1).

Terms

a(0) =4a(1) =35a(2) =252a(3) =1716a(4) =11440a(5) =75582a(6) =497420a(7) =3268760a(8) =21474180a(9) =141120525a(10) =927983760a(11) =6107086800a(12) =40225345056a(13) =265182149218