## 0.4 Stirling Numbers of the Second Kind

**OK but I knew all these things already.**

Here is a slight but useful modification. In D5 instead of the instruction
above put '=d$1*d4+c4', and copy that into a huge rectangle. The dollar sign,
$, will cause the index that follows it to remain constant. Thus when you copy
this into other rows and columns, d$1 will be the element of that column in
the first row.

When you again put 1 in c4 you get numbers called **"The Stirling numbers
of the second kind"**.

Binomial coefficients count the number of subsets of an n element set having
k elements in them. The Stirling number for arguments n and k here counts the
number of partitions of a set of n elements into k disjoint blocks.

**Exercises:**

**0.6 Set this up on your own machine.** Solution

**0.7 Binomial coefficients count the number of subsets of an n element set
having k elements in them. The Stirling number here counts the number of partitions
of a set of n elements into k disjoint blocks. Prove these two statements.** Solution

**0.8 Invent a good question for this spot.**