a(n) = 6*(2*n+1)! / ((n!)^2*(n+3)).

Terms

a(0) =2a(1) =9a(2) =36a(3) =140a(4) =540a(5) =2079a(6) =8008a(7) =30888a(8) =119340a(9) =461890a(10) =1790712a(11) =6953544a(12) =27041560a(13) =105306075a(14) =410605200a(15) =1602881040a(16) =6263890380a(17) =24502865310a(18) =95937144600a(19) =375945078600