auxiliary: Auxiliary functions for 'randtoolbox' package.
Description
Stirling numbers of the second kind and permutation of positive integers.
Usage
stirling(n)
permut(n)
Arguments
n
a positive integer.
Value
a vector with stirling numbers.
code
permut
eqn
$n=3$
itemize
tabular
c
cc
ccc
tab
2
2 1
1 2
3 2 1
1 3 2
2 3 1
1 2 3
2 1 3
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...}