a(n) = Sum_{k=0..floor(n/5)} (-1)^k * binomial(n-4*k,k) * Catalan(k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =0a(6) =-1a(7) =-2a(8) =-3a(9) =-4a(10) =-3a(11) =0a(12) =5a(13) =12a(14) =21a(15) =27a(16) =25a(17) =10a(18) =-23a(19) =-79a(20) =-149a(21) =-210a(22) =-225a(23) =-143a(24) =101a(25) =544a(26) =1153a(27) =1783a(28) =2135a(29) =1714