Closed form Formula for Partitions of an Integer

Question

I happened across the following question:

Determine the number of ways of putting $m$ indistinguishable balls into $n$ indistinguishable boxes with the restriction that no box is empty.

The obvious answer is $\Pi(m,n)$, where $\Pi$ denotes the partition of the positive integer $m$ into $n$ parts. This is not "satisfying". Is there a closed form formula for this $\Pi(m,n)$?

Answer 1

No, there is no known closed form for the partition function. Here is the sequence on OEIS, and also the Wolfram MathWorld page on this subject is very thorough.

Although, looking at this MathSE post, I might be wrong ...