a(n) = C(n)*(3n+2) where C(n) = Catalan numbers = A000108.

Terms

a(0) =2a(1) =5a(2) =16a(3) =55a(4) =196a(5) =714a(6) =2640a(7) =9867a(8) =37180a(9) =140998a(10) =537472a(11) =2057510a(12) =7904456a(13) =30458900a(14) =117675360a(15) =455657715a(16) =1767883500a(17) =6871173870a(18) =26747767200a(19) =104268528210a(20) =406975466040