a(n) = (-1)^[(n+1)/2] A000108([n/2]+1).

Terms

a(0) =1a(1) =-1a(2) =-2a(3) =2a(4) =5a(5) =-5a(6) =-14a(7) =14a(8) =42a(9) =-42a(10) =-132a(11) =132a(12) =429a(13) =-429a(14) =-1430a(15) =1430a(16) =4862a(17) =-4862a(18) =-16796a(19) =16796a(20) =58786a(21) =-58786a(22) =-208012a(23) =208012a(24) =742900a(25) =-742900a(26) =-2674440a(27) =2674440a(28) =9694845a(29) =-9694845