a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(2*k,2*n-6*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =2a(5) =0a(6) =3a(7) =18a(8) =3a(9) =4a(10) =60a(11) =60a(12) =9a(13) =140a(14) =350a(15) =146a(16) =275a(17) =1260a(18) =1267a(19) =732a(20) =3471a(21) =6476a(22) =4193a(23) =8470a(24) =24040a(25) =25104a(26) =24388a(27) =72810a(28) =117368a(29) =102672