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

Terms

a(0) =1a(1) =6a(2) =35a(3) =209a(4) =1275a(5) =7904a(6) =49589a(7) =313974a(8) =2002220a(9) =12841751a(10) =82752021a(11) =535345045a(12) =3474775708a(13) =22617821463a(14) =147584362683a(15) =965075220369