a(n) = floor((2*n)!/(n!^2*a(n-1))), with a(0)=1.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =11a(5) =22a(6) =42a(7) =81a(8) =158a(9) =307a(10) =601a(11) =1173a(12) =2305a(13) =4512a(14) =8891a(15) =17446a(16) =34453a(17) =67733a(18) =133983a(19) =263804a(20) =522533a(21) =1030093a(22) =2042630a(23) =4030798a(24) =8000302a(25) =15800729a(26) =31385800a(27) =62032493a(28) =123301357a(29) =243851870