If you first allocate the women on 20 predestined seats, then you have 20! possibilites to allocate them.
However, having an equidistant spacing of 1 seat between two women is only one in a few options. Let o be a woman, and x be a man:
This is your spacing. However,
also is a possible spacing. Now two men set besides each other, but that's okay.In fact, there are many other such spacings that are okay, which come out to , who would have guessed it, 21.
(The two equidistant spacings, the first where a woman is on the leftmost chair, the second where a man is on the leftmost chair. Then, for the seating with one "xx", you can swap that "xx" block with any other "x" block)
So, if you factor in the number of spacings to your calculation, you get the desired result: 21*20!*20!