a(n) = (3/n^3) * Sum_{d|n} (-1)^(n+d)*moebius(n/d)*binomial(2*d,d).

Terms

a(0) =6a(1) =3a(2) =2a(3) =3a(4) =6a(5) =13a(6) =30a(7) =75a(8) =200a(9) =555a(10) =1590a(11) =4693a(12) =14202a(13) =43863a(14) =137882a(15) =440235a(16) =1424958a(17) =4668304a(18) =15459366a(19) =51692379a(20) =174362770a(21) =592815459a(22) =2030105382a(23) =6998177293a(24) =24270836436a(25) =84646997613a(26) =296744311172