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

Terms

a(0) =1a(1) =1a(2) =0a(3) =-1a(4) =0a(5) =3a(6) =3a(7) =-5a(8) =-12a(9) =5a(10) =41a(11) =21a(12) =-110a(13) =-165a(14) =210a(15) =735a(16) =-30a(17) =-2505a(18) =-2205a(19) =6555a(20) =13710a(21) =-10035a(22) =-57390a(23) =-18471a(24) =185790a(25) =240793a(26) =-436317a(27) =-1276795a(28) =360302a(29) =4956495