Thread: s identical objects in n identical boxes - how many ways?

Hi, could someone help me with this problem - suppose I have s identical balls that I want to put in n identical boxes - in how many different way can I do this?

For example: s=3, n=3:

|ooo|||
|oo|o||
|o|o|o|

So the answer is 3.

s=6, n=2:

|oooooo||
|ooooo|o|
|oooo|oo|
|ooo|ooo|

So the answer is 4.

It's easy to do it ad hoc, but the general principle escapes me.

Thanks!

There is a recurrence relation, but no compact formula has been found yet.

Partition (number theory) - Wikipedia, the free encyclopedia

Bummer, I was hoping that there was an elegant solution to this problem. Thanks!

I'm not sure if the Wikipedia page has the recurrence the OP is after. We can sum the function P(n, k) given here

Partition Function P -- from Wolfram MathWorld

after equation (54) from 1 to k. Also, it's mentioned here, lower left cell

http://www.johndcook.com/TwelvefoldWay.pdf