pracma (version 1.5.8)

nchoosek: Binomial Coefficients

Description

Compute the Binomial coefficients.

Usage

nchoosek(n, k)

Arguments

n, k

integers with k between 0 and n

Value

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

Details

Alias for the corresponding R function choose.

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