a(n) = binomial(3*n,n) - binomial(3*n,n-3).

Terms

a(0) =1a(1) =3a(2) =15a(3) =83a(4) =483a(5) =2898a(6) =17748a(7) =110295a(8) =692967a(9) =4390815a(10) =28009215a(11) =179652564a(12) =1157534420a(13) =7486680048a(14) =48579667704a(15) =316107403839