How it is calculated
The items can be told apart, and the groups cannot. Four objects can therefore be split into two non-empty piles in seven ways, when the piles have no names.
S(n, k) = k × S(n − 1, k) + S(n − 1, k − 1)
Where the numbers come from
- Items
- Groups
Example
S(4, 2) = 7.
Questions
S(n, n) and S(n, 1)?
Both equal 1: either one each, or everyone in one group.
S(n, 0)?
Zero when n is greater than zero. S(0, 0) equals 1.
A ceiling?
25 items and 25 groups: beyond that the numbers get very large for this screen.