a(n) = Sum_{k=0..n} binomial(3*n-1,k).

Terms

a(0) =1a(1) =3a(2) =16a(3) =93a(4) =562a(5) =3473a(6) =21778a(7) =137980a(8) =880970a(9) =5658537a(10) =36519556a(11) =236618693a(12) =1538132224a(13) =10026362492a(14) =65513177704a(15) =428957009288