a(n) = C(n)*(10*n + 1) where C(n) = Catalan numbers (A000108).

Terms

a(0) =1a(1) =11a(2) =42a(3) =155a(4) =574a(5) =2142a(6) =8052a(7) =30459a(8) =115830a(9) =442442a(10) =1696396a(11) =6525246a(12) =25169452a(13) =97319900a(14) =377096040a(15) =1463921595a(16) =5692584870a(17) =22169259090a(18) =86452604700a(19) =337547269290