How the calculate the number of ways (permutation) of stacking m piles with n items?
Let's say I want 2 piles with 3 items: How to caluculates the permutations? A pile can consist of no item. What's to be considered is, that there are 2 places where an item can be placed. Legal combinations are:
o o x o o o o x
o x x o x o o x
x x x o x x o x
Not allowed is (Gravity needs to be considered):
x x
o o
x o
I thought catalan numbers could help. But I can't find a way to use them.