# Stirling Number of Number with Greater

## Theorem

Let $n, k \in \Z_{\ge 0}$.

Let $k > n$.

### Unsigned Stirling Number of the First Kind of Number with Greater

Let $\displaystyle {n \brack k}$ denote an unsigned Stirling number of the first kind.

Then:

$\displaystyle {n \brack k} = 0$

### 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 $\displaystyle \left\{ {n \atop k}\right\}$ denote a Stirling number of the second kind.

Then:

$\displaystyle \left\{ {n \atop k}\right\} = 0$