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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =12a(5) =15a(6) =21a(7) =126a(8) =420a(9) =804a(10) =1755a(11) =6270a(12) =19041a(13) =44616a(14) =111930a(15) =341523a(16) =986580a(17) =2540820a(18) =6745260a(19) =19430388a(20) =54887067a(21) =147559149a(22) =401839284a(23) =1133034441a(24) =3172437081a(25) =8698527090a(26) =23980954140a(27) =67114916895a(28) =187389089550a(29) =518670537840