What is the simplest way to find the coefficient of, for example, $\,x^{ 6 }$ in $\left(x+1\right)\cdot\left(x+2\right)\cdot \ldots\cdot\left(x+10\right)\,$? My teacher says that the easiest way is listing, but it doesn't help for high powers.
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1note that these coefficients are the definition of the (unsigned) Stirling numbers of the first kind. the specific example you give is $s(11,6)$. here 11 occurs instead of 10, as the Stirling polynomial has a factor of $x$ in addition to the ones you give. see also the Pochhammer symbol. – David Holden Aug 23 '15 at 23:18