a(n) = [x^n] (1 + x + x^2)^(3*n)/(1 + x)^(2*n).

Terms

a(0) =1a(1) =1a(2) =7a(3) =19a(4) =103a(5) =376a(6) =1825a(7) =7547a(8) =35175a(9) =153838a(10) =708132a(11) =3181091a(12) =14616481a(13) =66582283a(14) =306501377a(15) =1407473269a(16) =6497464679a(17) =29991098982a(18) =138844558150a(19) =643215119214