Stirling Number of n with n-m is Polynomial in n of Degree 2m/Second Kind
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Theorem
Let $m \in \Z_{\ge 0}$.
The Stirling number of the second kind $\displaystyle \left\{ {n \atop n - m}\right\}$ is a polynomial in $n$ of degree $2 m$.
Proof
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Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients