The number s(n,r) of ways of partitioning a set of n elements into r cycles. For example, the set {1,2,3,4} can be partitioned into two cycles in the following ways:

So s(4, 2) = 11. Clearly s(n,1) = (n−1)! and s(n, n) = 1. It can be shown that

Rather like the binomial coefficients, the Stirling numbers occur as coefficients in certain identities. They are named after the Scottish mathematician James Stirling (1692–1770).