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Binomial Coefficient

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Compute the binomial coefficient.

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

Factorial formula for the Binomial coefficient.

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


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


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


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 ) );


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.






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