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

Terms

a(0) =1a(1) =4a(2) =25a(3) =166a(4) =1125a(5) =7697a(6) =52933a(7) =365137a(8) =2523563a(9) =17462647a(10) =120937831a(11) =838016430a(12) =5809007778a(13) =40276886567a(14) =279303253405