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Oct 7, 2010 at 22:37 comment added Simon Rose I've already downloaded and skimmed over two of those, "stacked lattice boxes" and "partitions with designated summands" which don't seem to really help; they're mostly about the case where you simply count the number of such 'divisor partitions', instead of summing them. I could try email him though.
Oct 7, 2010 at 22:27 comment added Qiaochu Yuan Andrews might be a good person to ask directly; from reading some of his papers it looks like he's really interested in MacMahon's work.
Oct 7, 2010 at 22:24 history answered Gerry Myerson CC BY-SA 2.5