nchoosek: Binomial Coefficients

In pracma: Practical Numerical Math Functions

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

pracma documentation built on Nov. 10, 2023, 1:14 a.m.