[seqfan] Generalization of A005646

[franktaw at netscape.net]

I'm interested in generalizing A005646, and the associated triangle, to 
the case where more than 2-way partitions are allowed in making the 
classification.  We would want to require that each partition be 
completely essential; that is, combining any two parts in any partition 
would result in at least one pair of points being indistinguishable.

I don't have enough terms to even try looking this up to see if it is 
in the OEIS; I believe that it starts (from n = 1):

1,1,2,5

If it is present, it has neither a link to nor from A005646.

More terms, anyone?  Is there any literature on this question?

Franklin T. Adams-Watters