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

Terms

a(0) =1a(1) =3a(2) =6a(3) =10a(4) =25a(5) =81a(6) =238a(7) =596a(8) =1333a(9) =2827a(10) =5946a(11) =12618a(12) =26876a(13) =56821a(14) =118524a(15) =244016a(16) =497559a(17) =1008136a(18) =2033294a(19) =4083746a(20) =8166487a(21) =16259709a(22) =32240122a(23) =63689412a(24) =125402323a(25) =246179875a(26) =481955356a(27) =941114140a(28) =1833263243a(29) =3563030357