a(n) = binomial(2*(n+1),n) * gcd(n,2)/(2*(n+1)).

Terms

a(0) =1a(1) =1a(2) =5a(3) =7a(4) =42a(5) =66a(6) =429a(7) =715a(8) =4862a(9) =8398a(10) =58786a(11) =104006a(12) =742900a(13) =1337220a(14) =9694845a(15) =17678835a(16) =129644790a(17) =238819350a(18) =1767263190a(19) =3282060210a(20) =24466267020a(21) =45741281820a(22) =343059613650a(23) =644952073662