This function computes Stirling numbers of the second kind, S(n, k), which count the number of ways of partitioning n distinct objects in to k non-empty sets.
Usage
Stirling2(n, k)
S2(n, k)
Arguments
n
A vector of one or more positive integers
k
A vector of one or more positive integers
Details
The implementation on this function is a simple recurrence relation which defines
S(n, k) = kS(n - 1, k), + S(n - 1, k - 1)
for k > 0 with the inital conditions S(0, 0) = 1 and S(n, 0) = S(0, n) = 0. If n and n have different lengths then expand.grid is used to construct a vector of (n, k) pairs