It is an undergraduate exercise to show that the generating function for the sequence of unrestricted integer partitions $p(n)$ is the celebrated infinite product


$$\prod\_{k=1}^{\infty}\frac{1}{1-x^k}$$


More work has to be done if one wants to get asymptotic estimates of the function $p(n)$ (see for instance the pioneering work of Hardy and Ramanujan).


My question is the following: in the course of my research I have found the following generating function (which has a very similar aspect):


$$\prod\_{k=1}^{\infty}\frac{1}{(1-x^k)^k}$$


My question is if there are kwnown "natural" combinatorial families enumerated by this generating function. 


If yes, I will be happy to know some references.



An infinite product: combinatorial interpretation
This is called the MacMahon function, and counts plane =(3d, confusingly) partitions.


<http://en.wikipedia.org/wiki/Plane_partition>


