mathjs/docs/reference/functions/stirlingS2.md

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

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# Function stirlingS2

The Stirling numbers of the second kind, counts the number of ways to partition
a set of n labelled objects into k nonempty unlabelled subsets.
stirlingS2 only takes integer arguments.
The following condition must be enforced: k <= n.

 If n = k or k = 1 <= n, then s(n,k) = 1
 If k = 0 < n, then s(n,k) = 0

Note that if either n or k is supplied as a BigNumber, the result will be
as well.


## Syntax

```js
math.stirlingS2(n, k)
```

### Parameters

Parameter | Type | Description
--------- | ---- | -----------
`n` | Number &#124; BigNumber | Total number of objects in the set
`k` | Number &#124; BigNumber | Number of objects in the subset

### Returns

Type | Description
---- | -----------
Number &#124; BigNumber | S(n,k)


### Throws

Type | Description
---- | -----------


## Examples

```js
math.stirlingS2(5, 3) //returns 25
```


## See also

[bellNumbers](bellNumbers.md)