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I tried a lot, but couldn't find a way.
One thing which I found interesting is that
for n = 7, the maximum women can be
W W M W W M W = 5. Hope this might help someone to give an answer.

Omega Alpha
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    You say, $n$ men and $n$ women sit in $n$ seats... there are too many people to all sit down, are you saying that only some of the people will sit and others wont? Are your people considered distinct, or are they indistinguishable apart from gender? – JMoravitz May 15 '19 at 13:09
  • Yes according to question M M M M M M M is also a combination – Omega Alpha May 15 '19 at 13:10
  • all men are same and all women are same – Omega Alpha May 15 '19 at 13:11
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    See the linked question. Replace the flavor from being $1$'s and $0$'s, to being Men and Women respectively. – JMoravitz May 15 '19 at 13:12
  • Do you mean $m$ men and $w$ women in $n=m+w$ seats? You should be able to set up a set of recurrences and possibly give a generating function – Henry May 15 '19 at 13:12
  • @Henry no N men N women and N seats, some people will stay standing – Omega Alpha May 15 '19 at 13:14

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