a(n) = (-1)^n*Catalan(n).

Terms

a(0) =1a(1) =-1a(2) =2a(3) =-5a(4) =14a(5) =-42a(6) =132a(7) =-429a(8) =1430a(9) =-4862a(10) =16796a(11) =-58786a(12) =208012a(13) =-742900a(14) =2674440a(15) =-9694845a(16) =35357670a(17) =-129644790a(18) =477638700a(19) =-1767263190a(20) =6564120420a(21) =-24466267020a(22) =91482563640a(23) =-343059613650