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I wonder if there exists a formula for this function? $f(x) = (x-1)(x-2)(x-3) \cdots (x-k)$ I want to know the coefficient of each $x^i$, and the first thing I came up with was to find the expansion of this expression. Any idea?

Thanks,

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    @Arturo Magidin: You're just so right ^_^! Thank you.2011-04-15

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Look up the Stirling numbers and the falling factorial.

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    Alternatively, one can use Pochhammer symbols to represent these entities.2011-04-16