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

Terms

a(0) =1a(1) =2a(2) =2a(3) =0a(4) =-3a(5) =-2a(6) =9a(7) =24a(8) =11a(9) =-66a(10) =-152a(11) =-8a(12) =587a(13) =1082a(14) =-438a(15) =-5248a(16) =-7733a(17) =7942a(18) =47502a(19) =53792a(20) =-105313a(21) =-430118a(22) =-343043a(23) =1249800a(24) =3866557a(25) =1730018a(26) =-13996096a(27) =-34243896a(28) =-1947203a(29) =150962374