# Category:Factorials

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This category contains results about Factorials.

Definitions specific to this category can be found in Definitions/Factorials.

The **factorial of $n$** is defined inductively as:

- $n! = \begin{cases} 1 & : n = 0 \\ n \paren {n - 1}! & : n > 0 \end{cases}$

## Subcategories

This category has the following 18 subcategories, out of 18 total.

### D

### F

### G

### L

### R

### S

### W

## Pages in category "Factorials"

The following 61 pages are in this category, out of 61 total.

### D

### F

- Factorial as Product of Consecutive Factorials
- Factorial as Product of Consecutive Factorials/Lemma 1
- Factorial as Product of Consecutive Factorials/Lemma 2
- Factorial as Product of Three Factorials
- Factorial as Product of Two Factorials
- Factorial as Product of Two Factorials/Examples
- Factorial as Product of Two Factorials/Examples/3
- Factorial as Sum of Series of Subfactorial by Falling Factorial over Factorial
- Factorial Divides Product of Successive Numbers
- Factorial Divisible by Binary Root
- Factorial Divisible by Prime Power
- Factorial Greater than Cube for n Greater than 5
- Factorial Greater than Square for n Greater than 3
- Factorial of Integer plus Reciprocal of Integer
- Factorial which is Sum of Two Squares
- Falling Factorial as Quotient of Factorials

### L

### N

### P

### R

### S

- Sequence of Integers whose Factorial minus 1 is Prime
- Sequence of Integers whose Factorial plus 1 is Prime
- Smallest n needing 6 Numbers less than n so that Product of Factorials is Square
- Stirling's Formula
- Stirling's Formula/Examples
- Sum of Factorials of Digits of 169
- Sum of Sequence of Alternating Positive and Negative Factorials being Prime
- Sum of Sequence of Factorials
- Sum of Sequence of k x k!
- Sum over k to n of Unsigned Stirling Number of the First Kind of k with m by n factorial over k factorial
- Summation over k to n of Natural Logarithm of k
- Summation over Lower Index of Unsigned Stirling Numbers of the First Kind
- Summation over Lower Index of Unsigned Stirling Numbers of the First Kind with Alternating Signs