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

Terms

a(0) =3a(1) =3a(2) =9a(3) =30a(4) =120a(5) =513a(6) =2373a(7) =11484a(8) =57861a(9) =300420a(10) =1599477a(11) =8692074a(12) =48061689a(13) =269694453a(14) =1532744100a(15) =8808000696a(16) =51110965698a(17) =299155382325