a(n) = floor((3*n)!/(n!^3*a(n-1))), where a(0)=1.

Terms

a(0) =1a(1) =6a(2) =15a(3) =112a(4) =309a(5) =2449a(6) =7004a(7) =56977a(8) =166128a(9) =1371673a(10) =4046880a(11) =33736358a(12) =100328902a(13) =842011587a(14) =2518460195a(15) =21241145637a(16) =63807550099a(17) =540215987658