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In 1996, my brilliant student John Noonan, discovered, and proved that thereare 3(2n)!/(n(n+3)!(n-3)!) ways to line-up n people of different heights insuch a way that out of the n(n-1)(n-2)/6 possible triples of people exactly oneis such that the tallest stands (not necessarily immediately) in front of thesecond-tallest, who in turn, stands (not necessarily immediately) in front ofthe shortest. In that article, I promised a prize of 25 dollars for a nicecombinatorial proof. Alex Burstein gave such a proof. On Oct. 14, 2011, Italked about Alex's lovely proof at the Howard U. math colloquium, and publiclypresented the 25-dollar prize. The present note is the outcome. CongratulationsAlex!

Alexander Burstein's Lovely Combinatorial Proof of John Noonan's  Beautiful Formula that the number of n-permutations that contain the Pattern  321 Exactly Once Equals (3/n)(2n)!/((n-3)!(n+3)!)