Stirling numbers of the first kind

The Stirling numbers of the first kind s(n, k) count the number of ways to permute a list of n items into k cycles.

For example, the list {1, 2, 3, 4} can be permuted into two cycles in the following ways:

There are 11 such permutations, thus s(4, 2) = 11.

Here are some illegible diagrams showing the cycles for permutations of a list with five elements.

s(5, 1) = 24:
(sorry, not much without pictures)

s(5, 2) = 50:

s(5, 3) = 35:

s(5, 4) = 10:

s(5, 5) = 1:

Designed and rendered using Mathematica 3.0 for NeXT.