Binomial Coefficient

Compute the binomial coefficient.

The binomial coefficient of two nonnegative integers n and k is defined as

The binomial coefficient can be generalized to negative integers n as follows:

Installation

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

Usage

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

binomcoef( n, k )

Evaluates the binomial coefficient of two integers n and k.

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.

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

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

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

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

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

Examples

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 );

C APIs

Usage

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

stdlib_base_binomcoef( n, k )

Evaluates the binomial coefficient of two integers n and k.

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.

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

Examples

#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 );
    }
}

Notice

This package is part of 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, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.