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

Terms

a(0) =1a(1) =2a(2) =2a(3) =2a(4) =3a(5) =3a(6) =2a(7) =4a(8) =5a(9) =0a(10) =4a(11) =13a(12) =-7a(13) =-7a(14) =48a(15) =-16a(16) =-93a(17) =180a(18) =74a(19) =-584a(20) =517a(21) =1111a(22) =-2850a(23) =207a(24) =8281a(25) =-10738a(26) =-11740a(27) =46967a(28) =-22167a(29) =-115845