a(n) = (1/n^2) * Sum_{d|n} moebius(n/d)*binomial(2*d,d).

Terms

a(0) =2a(1) =1a(2) =2a(3) =4a(4) =10a(5) =25a(6) =70a(7) =200a(8) =600a(9) =1845a(10) =5830a(11) =18772a(12) =61542a(13) =204659a(14) =689410a(15) =2347920a(16) =8074762a(17) =28009524a(18) =97909318a(19) =344615860a(20) =1220539390a(21) =4347310451a(22) =15564141262a(23) =55985418344a(24) =202256970300a(25) =733607281875