a(n) = (11*n + 3 + 6/(n+2)) * Catalan(n).

Terms

a(0) =6a(1) =16a(2) =53a(3) =186a(4) =672a(5) =2472a(6) =9207a(7) =34606a(8) =130988a(9) =498576a(10) =1906346a(11) =7316596a(12) =28170768a(13) =108760560a(14) =420889995a(15) =1632155670a(16) =6340808820a(17) =24673450560a(18) =96148670310a(19) =375164728620