Stirling Number of Number with Greater
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Theorem
Let $n, k \in \Z_{\ge 0}$.
Let $k > n$.
Unsigned Stirling Number of the First Kind of Number with Greater
Let $\ds {n \brack k}$ denote an unsigned Stirling number of the first kind.
Then:
- $\ds {n \brack k} = 0$
Signed Stirling Number of the First Kind of Number with Greater
Let $\map s {n, k}$ denote a signed Stirling number of the first kind.
Then:
- $\map s {n, k} = 0$
Stirling Number of the Second Kind of Number with Greater
Let $\ds {n \brace k}$ denote a Stirling number of the second kind.
Then:
- $\ds {n \brace k} = 0$