[seqfan] Regarding A122172 - A proper definition is needed for this sequence

[David Scambler]

Part of the problem with presenting this sequence is that it is an infinite sequence of rectangular arrays, not of integers.

The j'th array in the triangle has j+1 columns and partitions(j) rows.

Each row of the j'th section corresponds to a partition of j and answers the following question:

How many ways may 0<=k<=j indistinguishable balls be dropped into a set of urns whose maximum capacities 
are determined by the parts of a partition of j?

e.g. j = 3

Urns   k= 0 1 2 3 
========  =======
(3)       1 1 1 1
(2)(1)    1 2 2 1
(1)(1)(1) 1 3 3 1

dave