npm package: @stdlib/math-base-special-binomcoef
Description: Compute the binomial coefficient.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Binomial Coefficient

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the [binomial coefficient][binomial-coefficient].

<section class="intro">

The [binomial coefficient][binomial-coefficient] of two nonnegative integers `n` and `k` is defined as

<!-- <equation class="equation" label="eq:binomial_coefficient" align="center" raw="\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n" alt="Factorial formula for the Binomial coefficient."> -->

<div class="equation" align="center" data-raw-text="\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n" data-equation="eq:binomial_coefficient">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/binomcoef/docs/img/equation_binomial_coefficient.svg" alt="Factorial formula for the Binomial coefficient.">
    <br>
</div> -->

<!-- </equation> -->

The [binomial coefficient][binomial-coefficient] can be generalized to negative integers `n` as follows:

<!-- <equation class="equation" label="eq:binomial_coefficient_negative_integers" align="center" raw="\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)" alt="Generalization of the binomial coefficient to negative n."> -->

<!-- <div class="equation" align="center" data-raw-text="\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)" data-equation="eq:binomial_coefficient_negative_integers">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/math/base/special/binomcoef/docs/img/equation_binomial_coefficient_negative_integers.svg" alt="Generalization of the binomial coefficient to negative n.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-binomcoef
```

</section>

<section class="usage">

## Usage

```javascript
var binomcoef = require( '@stdlib/math-base-special-binomcoef' );
```

#### binomcoef( n, k )

Evaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.

```javascript
var v = binomcoef( 8, 2 );
// returns 28

v = binomcoef( 0, 0 );
// returns 1

v = binomcoef( -4, 2 );
// returns 10

v = binomcoef( 5, 3 );
// returns 10

v = binomcoef( NaN, 3 );
// returns NaN

v = binomcoef( 5, NaN );
// returns NaN

v = binomcoef( NaN, NaN );
// returns NaN
```

For negative `k`, the function returns `0`.

```javascript
var v = binomcoef( 2, -1 );
// returns 0

v = binomcoef( -3, -1 );
// returns 0
```

The function returns `NaN` for non-integer `n` or `k`.

```javascript
var v = binomcoef( 2, 1.5 );
// returns NaN

v = binomcoef( 5.5, 2 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var binomcoef = require( '@stdlib/math-base-special-binomcoef' );

var opts = {
    'dtype': 'float64'
};
var n = discreteUniform( 100, -10, 30, opts );
var k = discreteUniform( 100, 0, 20, opts );

logEachMap( '%d choose %d = %d', n, k, binomcoef );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/binomcoef.h"
```

#### stdlib_base_binomcoef( n, k )

Evaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.

```c
double v = stdlib_base_binomcoef( 8.0, 2.0 );
// returns 28.0
```

The function accepts the following arguments:

-   **n**: `[in] double` input value.
-   **k**: `[in] double` input value.

```c
double stdlib_base_binomcoef( const double n, const double k );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/binomcoef.h"
#include <stdio.h>

int main( void ) {
    const double a[] = { 24.0, 32.0, 48.0, 116.0, 33.0 };
    const double b[] = { 12.0, 6.0, 15.0, 52.0, 22.0 };

    double out;
    int i;
    for ( i = 0; i < 5; i++ ) {
        out = stdlib_base_binomcoef( a[ i ], b[ i ] );
        printf( "binomcoef(%lf, %lf) = %lf\n", a[ i ], b[ i ], out );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[binomial-coefficient]: https://en.wikipedia.org/wiki/Binomial_coefficient

</section>

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