  Why bother with fully rigorous proofs when one can very quickly get
semi-rigorous ones? Yes, yes, we know how to get a "rigorous" proof of the
result stated in the title of this article. One way is the boring, human one,
citing some heavy guns of theorems that already exist in the literature. We
also know how to get a fully rigorous proof automatically, using the methods in
this http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/georgy.htm neat
article (but it would be a little more complicated, since the probability
generating polynomial is not "closed form" but satisfies a second-order
recurrence gotten from the Zeilberger algorithm), otherwise the same method
would work, alas, it is not yet implemented.
  Instead, we chose to use the great Maple package
http://www.math.rutgers.edu/~zeilberg/tokhniot/HISTABRUT">HISTABRUT(in fact, a
very tiny part of it, procedure AlphaSeq), explained in this other
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/histabrut.html">neat
article, and get a semi-rigorous proof. We also needed the nice little Maple
package http://www.math.rutgers.edu/~zeilberg/tokhniot/GuessRat">GuessRat, to
do the guessing of rational functions.
  Equipped with these two packages, Zeilberger wrote a short Maple program
http://www.math.rutgers.edu/~zeilberg/tokhniot/SameSexMarriages">SameSexMarriages
that enabled the author to generate this paper.
