# auxfun: Auxiliary functions for 'randtoolbox' package. In randtoolbox: Toolbox for Pseudo and Quasi Random Number Generation and RNG Tests

## Description

Stirling numbers of the second kind and permutation of positive integers.

## Usage

 ```1 2``` ```stirling(n) permut(n) ```

## Arguments

 `n` a positive integer.

## Details

`stirling` computes stirling numbers of second kind i.e.

Stirl_n^k = k * Stirl_{n-1}^k + Stirl_{n-1}^{k-1}

with Stirl_n^1 = Stirl_n^n = 1. e.g.

• n = 0, returns 1

• n = 1, returns a vector with 0,1

• n = 2, returns a vector with 0,1,1

• n = 3, returns a vector with 0,1,3,1

• n = 4, returns a vector with 0,1,7,6,1...

Go to wikipedia for more details.

`permut` compute permutation of {1, ..., n} and store it in a matrix. e.g.

• n=1, returns a matrix with

 1
• n=2, returns a matrix with

 1 2 2 1
• n=3 returns a matrix with

 3 1 2 3 2 1 1 3 2 2 3 1 1 2 3 2 1 3

## Value

a vector with stirling numbers.

## Author(s)

Christophe Dutang.

`choose` for combination numbers.
 ```1 2 3 4 5``` ```# should be 1 stirling(0) # should be 0,1,7,6,1 stirling(4) ```