Interpreting a formula from Graph Theory - where do x and y come from?

I'm trying to understand the generating function for OEIS A062734, which is in Mathematica. Essentially, despite knowing no Mathematica at all, I think I can parse most of it, but where do $x$ and $y$ come from?

nn = 6;
s = Sum[(1+y)^Binomial[n, 2] x^n/n!, {n, 0, nn}];
Range[0, nn]!CoefficientList[Series[Log[ s]+1, {x, 0, nn}], {x, y}]//Grid
(* returns triangle indexed at n = 0, Geoffrey Critzer, Oct 07 2012 *)


The history of the page isn't much help, and the non-Mathematica formula is very similar. Apologies for the probably completely trivial question.

Without being expert in the field, it seems that the required numbers can be expressed as the coefficients of a two-variable polynomial. So $x$ and $y$ are only used to create that polynomial (Why and how is a different thing, though). They have no other purpose and are of no interest later on.
• FYI this is called a generating function. It does serve some purpose and is of great interest in mathematics. For example, the variables $x$ and $y$ could be specialized. If you set $y=1$, you recover oeis.org/A001187 . – Kellen Myers Dec 8 '14 at 21:47