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 followingways:

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:
s1 5 1

s(5, 2) = 50:
s1 5 2

s(5, 3) = 35:
s1 5 3

s(5, 4) = 10:
s1 5 4