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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =13a(6) =35a(7) =100a(8) =300a(9) =925a(10) =2915a(11) =9386a(12) =30771a(13) =102347a(14) =344705a(15) =1173960a(16) =4037381a(17) =14004912a(18) =48954659a(19) =172307930a(20) =610269695a(21) =2173656683a(22) =7782070631a(23) =27992709172a(24) =101128485150a(25) =366803656323