a(n) = Sum_{k=0..n} binomial(3*n+2*k+2,n-k).

Terms

a(0) =1a(1) =6a(2) =39a(3) =259a(4) =1735a(5) =11673a(6) =78729a(7) =531797a(8) =3595726a(9) =24328695a(10) =164685250a(11) =1115156661a(12) =7553047301a(13) =51166448965a(14) =346660659576