A246604 (Catalan(n)-n) with initial terms 1,0,0,2,10 changed to 1,1,1,2,11.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =11a(5) =37a(6) =126a(7) =422a(8) =1422a(9) =4853a(10) =16786a(11) =58775a(12) =208000a(13) =742887a(14) =2674426a(15) =9694830a(16) =35357654a(17) =129644773a(18) =477638682a(19) =1767263171a(20) =6564120400a(21) =24466266999a(22) =91482563618a(23) =343059613627