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I created a stub for falling factorial, mainly to record the simple fact I learned yesterday that it counts the number of injections between two finite sets.
I added some more material (some of which was also at binomial theorem), mainly about the context of finite difference calculus.
Excellent, thanks! These additional properties you mention seem to advocate the notation $n^{\underline{k}}$ which you used for the falling factorial at binomial theorem – would you prefer to use that as the main notation in this article as well?
Thanks for asking! That is my own preference, yes.
Done.
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