a(n) = C(n) if n is odd, else C(n) - C(n/2); C(n) are Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =5a(3) =12a(4) =42a(5) =127a(6) =429a(7) =1416a(8) =4862a(9) =16754a(10) =58786a(11) =207880a(12) =742900a(13) =2674011a(14) =9694845a(15) =35356240a(16) =129644790a(17) =477633838a(18) =1767263190a(19) =6564103624a(20) =24466267020a(21) =91482504854a(22) =343059613650