https://github.com/cran/pracma
Tip revision: e2512490ec9e26c0bfb230f9fd97bcf07cc8c07b authored by Hans W. Borchers on 10 November 2023, 00:10:02 UTC
version 2.4.4
version 2.4.4
Tip revision: e251249
nchoosek.Rd
\name{nchoosek}
\alias{nchoosek}
\title{
Binomial Coefficients
}
\description{
Compute the Binomial coefficients.
}
\usage{
nchoosek(n, k)
}
\arguments{
\item{n, k}{integers with \code{k} between 0 and \code{n}}
}
\details{
Alias for the corresponding R function \code{choose}.
}
\value{
integer, the Binomial coefficient \eqn{({n \over k})}.
}
\note{
In Matlab/Octave, if \code{n} is a vector all combinations of \code{k}
elements from vector \code{n} will be generated. Here, use the function
\code{combs} instead.
}
\seealso{
\code{\link{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
}
\keyword{ arith }