a(n) = 6 * (4*n)! / ((n+1)! * (3*n+1)!).

Terms

a(0) =6a(1) =3a(2) =8a(3) =33a(4) =168a(5) =969a(6) =6072a(7) =40365a(8) =280488a(9) =2017356a(10) =14914848a(11) =112784399a(12) =869046168a(13) =6803716710a(14) =53997506640a(15) =433647466245