a(n) = C(n)*(12n+1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =13a(2) =50a(3) =185a(4) =686a(5) =2562a(6) =9636a(7) =36465a(8) =138710a(9) =529958a(10) =2032316a(11) =7818538a(12) =30161740a(13) =116635300a(14) =451980360a(15) =1754766945a(16) =6824030310a(17) =26577181950a(18) =103647597900a(19) =404703270510