a(n) = (2/(3*n-1))*binomial(3*n,n).

Terms

a(0) =-2a(1) =3a(2) =6a(3) =21a(4) =90a(5) =429a(6) =2184a(7) =11628a(8) =63954a(9) =360525a(10) =2072070a(11) =12096045a(12) =71524440a(13) =427496076a(14) =2578547760a(15) =15675792072a(16) =95951017602a(17) =590842763469