No, n!*n! is not equal to nor simply related to (2n)!. Just look at some values: if n= 2, 2!*2!= 4 while (2(2))!= 4!= 24. If n= 3, 3!*3!= 36 while (2(3))!= 6!= 720. You should be able to show that n!n! always divides (2n)! but there is no closer relationship than that.