a(n) = 3*binomial(3*n+9, n)/(n+3).

Terms

a(0) =1a(1) =9a(2) =63a(3) =408a(4) =2565a(5) =15939a(6) =98670a(7) =610740a(8) =3786588a(9) =23535820a(10) =146710476a(11) =917263152a(12) =5752004349a(13) =36174046743a(14) =228124619100