a(n) = gcd(n!!, (n-1)!!) where n!! = A006882.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =3a(7) =3a(8) =3a(9) =3a(10) =15a(11) =15a(12) =45a(13) =45a(14) =315a(15) =315a(16) =315a(17) =315a(18) =2835a(19) =2835a(20) =14175a(21) =14175a(22) =155925a(23) =155925a(24) =467775a(25) =467775a(26) =6081075a(27) =6081075a(28) =42567525a(29) =42567525