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

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =-1a(5) =-2a(6) =-1a(7) =2a(8) =7a(9) =9a(10) =3a(11) =-16a(12) =-39a(13) =-43a(14) =9a(15) =126a(16) =247a(17) =199a(18) =-213a(19) =-984a(20) =-1555a(21) =-756a(22) =2525a(23) =7518a(24) =9593a(25) =559a(26) =-24899a(27) =-56216a(28) =-55241a(29) =33150