a(n) = Catalan(n) - A000245(n-2).

Terms

a(0) =2a(1) =4a(2) =11a(3) =33a(4) =104a(5) =339a(6) =1133a(7) =3861a(8) =13364a(9) =46852a(10) =166022a(11) =593674a(12) =2139552a(13) =7763305a(14) =28337265a(15) =103981965a(16) =383351580a(17) =1419269280a(18) =5274495930a(19) =19669409790a(20) =73580417040a(21) =276043317030