a(n) = n!/ceiling(n/2)!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =12a(5) =20a(6) =120a(7) =210a(8) =1680a(9) =3024a(10) =30240a(11) =55440a(12) =665280a(13) =1235520a(14) =17297280a(15) =32432400a(16) =518918400a(17) =980179200a(18) =17643225600a(19) =33522128640a(20) =670442572800