The least positive integer k for which the value k×n2(n2−12)(n2−22)....(n2−(n−1)2) turns into a factorial of some positive integer is
2
k×n2(n−1)(n+1)(n−2)(n+2)....(n+n−1)(n−n+1)=r!
k×n.1.2.3.4....(n−1)n(n+1).....(2n−1)=r!
k×n(2n−1)!=r!
If k = 2 then L.H.S = (2n)! = r!