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

Terms

a(0) =1a(1) =0a(2) =3a(3) =0a(4) =6a(5) =0a(6) =10a(7) =10a(8) =15a(9) =60a(10) =21a(11) =210a(12) =28a(13) =560a(14) =64a(15) =1260a(16) =297a(17) =2520a(18) =1315a(19) =4620a(20) =4686a(21) =7975a(22) =13938a(23) =13530a(24) =36127a(25) =24310a(26) =84189a(27) =50050a(28) =180391a(29) =118755