# Category:Examples of Stirling Numbers of the First Kind

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This category contains examples of Stirling Numbers of the First Kind.

### Unsigned Stirling Numbers of the First Kind

**Unsigned Stirling numbers of the first kind** are defined recursively by:

- $\displaystyle {n \brack k} := \begin{cases} \delta_{n k} & : k = 0 \text { or } n = 0 \\ & \\ \displaystyle {n - 1 \brack k - 1} + \paren {n - 1} {n - 1 \brack k} & : \text{otherwise} \\ \end{cases}$

### Signed Stirling Numbers of the First Kind

**Signed Stirling numbers of the first kind** are defined recursively by:

- $\map s {n, k} := \begin{cases} \delta_{n k} & : k = 0 \text{ or } n = 0 \\ \map s {n - 1, k - 1} - \paren {n - 1} \map s {n - 1, k} & : \text{otherwise} \\ \end{cases}$

## Pages in category "Examples of Stirling Numbers of the First Kind"

The following 17 pages are in this category, out of 17 total.

### P

### S

- Signed Stirling Number of the First Kind of 0
- Signed Stirling Number of the First Kind of 1
- Signed Stirling Number of the First Kind of n with n-1
- Signed Stirling Number of the First Kind of n+1 with 0
- Signed Stirling Number of the First Kind of n+1 with 1
- Signed Stirling Number of the First Kind of Number with Self
- Stirling Numbers of the First Kind/Examples
- Stirling Numbers of the First Kind/Examples/5th Falling Factorial

### U

- Unsigned Stirling Number of the First Kind of 0
- Unsigned Stirling Number of the First Kind of 1
- Unsigned Stirling Number of the First Kind of n with n-1
- Unsigned Stirling Number of the First Kind of n with n-2
- Unsigned Stirling Number of the First Kind of n with n-3
- Unsigned Stirling Number of the First Kind of n+1 with 0
- Unsigned Stirling Number of the First Kind of n+1 with 1