Compute the binomial coefficient.
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Compute the [binomial coefficient][binomial-coefficient].
n and k is defined asmath
\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq nn as follows:math
\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)bash
npm install @stdlib/math-base-special-binomcoefscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var binomcoef = require( '@stdlib/math-base-special-binomcoef' );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 NaNk, the function returns 0.javascript
var v = binomcoef( 2, -1 );
// returns 0
v = binomcoef( -3, -1 );
// returns 0NaN for non-integer n or k.javascript
var v = binomcoef( 2, 1.5 );
// returns NaN
v = binomcoef( 5.5, 2 );
// returns NaNjavascript
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
#include "stdlib/math/base/special/binomcoef.h"n and k.c
double v = stdlib_base_binomcoef( 8, 2 );
// returns 28.0[in] int64_t input value.[in] int64_t input value.c
double stdlib_base_binomcoef( const int64_t n, const int64_t k );c
#include "stdlib/math/base/special/binomcoef.h"
#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>
int main( void ) {
const int64_t a[] = { 24, 32, 48, 116, 33 };
const int64_t b[] = { 12, 6, 15, 52, 22 };
double out;
int i;
for ( i = 0; i < 5; i++ ) {
out = stdlib_base_binomcoef( a[ i ], b[ i ] );
printf( "binomcoef(%" PRId64 ", %" PRId64 ") = %lf\n", a[ i ], b[ i ], out );
}
}
