Catalan numbers minus odd-indexed Fibonacci numbers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =8a(5) =43a(6) =196a(7) =820a(8) =3265a(9) =12615a(10) =47840a(11) =179355a(12) =667875a(13) =2478022a(14) =9180616a(15) =34011401a(16) =126120212a(17) =468411235a(18) =1743105373a(19) =6500874434a(20) =24300686879a(21) =91049069203a(22) =341924710480