R: Binomial Coefficients

nchoosek {pracma} | R Documentation

## Binomial Coefficients

### Description

Compute the Binomial coefficients.

### Usage

    nchoosek(n, k)

### Arguments

`n, k` | integers with `k` between 0 and `n`

### Details

Alias for the corresponding R function `choose`.

### Value

integer, the Binomial coefficient ({n \over k}).

### Note

In Matlab/Octave, if `n` is a vector all combinations of `k` elements from vector `n` will be generated. Here, use the function `combs` instead.

### See Also

`choose`

### Examples

    S <- sapply(0:6, function(k) nchoosek(6, k))  # 1  6 15 20 15  6  1

    # Catalan numbers
    catalan <- function(n) choose(2*n, n)/(n+1)
    catalan(0:10)
    # 1  1  2  5  14  42  132  429  1430  4862  16796

    # Relations
    n <- 10
    sum((-1)^c(0:n) * sapply(0:n, function(k) nchoosek(n, k)))  # 0

[Package pracma version 2.0.4 Index]