a(n) = Sum_{k = 0..n} binomial(n,floor(k/2))*(-1)^(n-k).

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =6a(5) =0a(6) =20a(7) =0a(8) =70a(9) =0a(10) =252a(11) =0a(12) =924a(13) =0a(14) =3432a(15) =0a(16) =12870a(17) =0a(18) =48620a(19) =0a(20) =184756a(21) =0a(22) =705432a(23) =0a(24) =2704156a(25) =0a(26) =10400600a(27) =0a(28) =40116600a(29) =0