A transformation of the Catalan sequence.

Terms

a(0) =1a(1) =2a(2) =1a(3) =-1a(4) =1a(5) =6a(6) =1a(7) =-13a(8) =1a(9) =43a(10) =1a(11) =-131a(12) =1a(13) =430a(14) =1a(15) =-1429a(16) =1a(17) =4863a(18) =1a(19) =-16795a(20) =1a(21) =58787a(22) =1a(23) =-208011a(24) =1a(25) =742901a(26) =1a(27) =-2674439a(28) =1a(29) =9694846