Catalan number A000108(n) minus Motzkin number A001006(n).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =5a(5) =21a(6) =81a(7) =302a(8) =1107a(9) =4027a(10) =14608a(11) =52988a(12) =192501a(13) =701065a(14) =2560806a(15) =9384273a(16) =34504203a(17) =127288011a(18) =471102318a(19) =1749063906a(20) =6513268401a(21) =24323719461a(22) =91081800417a(23) =341929853235