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

Terms

a(0) =1a(1) =4a(2) =21a(3) =120a(4) =715a(5) =4368a(6) =27132a(7) =170544a(8) =1081575a(9) =6906900a(10) =44352165a(11) =286097760a(12) =1852482996a(13) =12033222880a(14) =78378960360a(15) =511738760544