a(n) = B(2n,3)/B(2n) (see comment).

Terms

a(0) =1a(1) =15a(2) =141a(3) =1275a(4) =11481a(5) =103335a(6) =930021a(7) =8370195a(8) =75331761a(9) =677985855a(10) =6101872701a(11) =54916854315a(12) =494251688841