Stirling Number of n with n-m is Polynomial in n of Degree 2m/Second Kind

Theorem

Let $m \in \Z_{\ge 0}$.

The Stirling number of the second kind $\ds {n \brace n - m}$ 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