Rising and Falling Factorials
Let represent the rising factorial and let represent the falling factorial .
Then and
For example,
Compare the third row of the table of values.
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“When I, sitting, heard the astronomer, where he lectured with such applause in the lecture room,
How soon, unaccountable, I became tired and sick;
Till rising and gliding out, I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.”
—Walt Whitman (1819–1892)
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