How Many Ways to Partition N Balls into Subgroups with a Maximum of k Balls?

[guyov1]

Hello.
I am trying to find out the number of options to divide N balls to subgroups in a way that each subgroup does not contain more than k balls.

Any idea?
Thanks!

 

[CRGreathouse]

k = 0: http://www.research.att.com/~njas/sequences/A000007
k = 1: http://www.research.att.com/~njas/sequences/A000012
k = 2: http://www.research.att.com/~njas/sequences/A008619
k = 3: http://www.research.att.com/~njas/sequences/A001399
k = 4: http://www.research.att.com/~njas/sequences/A001400
k = 5: http://www.research.att.com/~njas/sequences/A001401
k = 6: http://www.research.att.com/~njas/sequences/A001402
k = 7: http://www.research.att.com/~njas/sequences/A008636

http://www.research.att.com/~njas/sequences/A008284 is the whole triangle.