Number of Dyck bridges with resets from any height to zero from (0,0) to (n,0).

Terms

a(0) =1a(1) =1a(2) =5a(3) =11a(4) =39a(5) =105a(6) =335a(7) =965a(8) =2965a(9) =8755a(10) =26517a(11) =79047a(12) =238065a(13) =712347a(14) =2140473a(15) =6414555a(16) =19256535a(17) =57743865a(18) =173280215a(19) =519743405a(20) =1559414971a(21) =4677875401a(22) =14034331635a(23) =42101584041a(24) =126307456279a(25) =378916960525