Divisibility property of binomial coefficients (Hoggatt triangles)

tchow_at_lsa.umich.edu
Date: 08/20/04 

Date: 20 Aug 2004 11:15:00 -0400

Is it true, and if so how does one prove, that

   (n choose m) * (n choose m+1) * ... * (n choose m+k)

is divisible by

   (n choose 0) * (n choose 1) * ... * (n choose k) ?

This problem is associated with so-called "Hoggatt triangles" and
"Hoggatt sequences" but the papers containing those keywords appear
to assert the above divisibility property without proof. 

-- 
Tim Chow       tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth.  ---Galileo, Dialogues Concerning Two New Sciences