# Binomial Coefficient
> Compute the [binomial coefficient][binomial-coefficient].
The [binomial coefficient][binomial-coefficient] of two nonnegative integers `n` and `k` is defined as
The [binomial coefficient][binomial-coefficient] can be generalized to negative integers `n` as follows:
## 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
```
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var binomcoef = require( '@stdlib/math/base/special/binomcoef' );
var n;
var k;
var i;
for ( i = 0; i < 100; i++ ) {
n = round( (randu()*30.0) - 10.0 );
k = round( randu()*20.0 );
console.log( '%d choose %d = %d', n, k, binomcoef( n, k ) );
}
```
[binomial-coefficient]: https://en.wikipedia.org/wiki/Binomial_coefficient
