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

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =-15a(5) =-99a(6) =-398a(7) =-1175a(8) =-2351a(9) =0a(10) =29601a(11) =183195a(12) =756978a(13) =2351805a(14) =4885791a(15) =0a(16) =-63746991a(17) =-400000275a(18) =-1675991918a(19) =-5274560891a(20) =-11081420615a(21) =0a(22) =147257373891a(23) =931226954949a(27) =0