a(n) = C(n)*(9*n + 1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =10a(2) =38a(3) =140a(4) =518a(5) =1932a(6) =7260a(7) =27456a(8) =104390a(9) =398684a(10) =1528436a(11) =5878600a(12) =22673308a(13) =87662200a(14) =339653880a(15) =1318498920a(16) =5126862150a(17) =19965297660a(18) =77855108100a(19) =303969268680