A transform of the Catalan numbers with a simple Hankel transform.

Terms

a(0) =1a(1) =0a(2) =-1a(3) =-1a(4) =1a(5) =2a(6) =1a(7) =-3a(8) =-5a(9) =-1a(10) =11a(11) =15a(12) =-5a(13) =-44a(14) =-41a(15) =51a(16) =169a(17) =85a(18) =-303a(19) =-611a(20) =-15a(21) =1513a(22) =2021a(23) =-1271a(24) =-6827a(25) =-5673a(26) =10361a(27) =28301a(28) =10141a(29) =-61102