Binomial Coefficient

Compute the binomial coefficient.

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

StartBinomialOrMatrix n Choose k EndBinomialOrMatrix equals StartFraction n factorial Over k factorial left-parenthesis n minus k right-parenthesis factorial EndFraction for 0 less-than-or-equal-to k less-than-or-equal-to n

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

StartBinomialOrMatrix negative n Choose k EndBinomialOrMatrix equals left-parenthesis negative 1 right-parenthesis Superscript k Baseline StartBinomialOrMatrix n plus k minus 1 Choose k EndBinomialOrMatrix equals left-parenthesis negative 1 right-parenthesis Superscript k Baseline left-parenthesis StartBinomialOrMatrix n Choose k EndBinomialOrMatrix right-parenthesis

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 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 ) );
}