n*a(n) provides the Moebius transform of signed central binomial coefficients.

Terms

a(0) =1a(1) =-1a(2) =-1a(3) =1a(4) =1a(5) =-1a(6) =-3a(7) =4a(8) =8a(9) =-13a(10) =-23a(11) =39a(12) =71a(13) =-121a(14) =-229a(15) =400a(16) =757a(17) =-1354a(18) =-2559a(19) =4625a(20) =8799a(21) =-16021a(22) =-30671a(23) =56316a(24) =108166a(25) =-200047a(26) =-385210a(27) =716429a(28) =1383331a(29) =-2585173