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.


1 Answer 1


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.

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    $\begingroup$ I completely missed the fact that they were supposed to be interpreted symbolically. Thanks! $\endgroup$ Dec 8, 2014 at 11:17
  • $\begingroup$ 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 . $\endgroup$ Dec 8, 2014 at 21:47
  • $\begingroup$ @KellenMyers Thanks for the info. In principle I know what a generating function is; I only wanted to say that I am not really into Graph Theory to explain further details on that one. If you have a link to a more general treatment of this topic, please tell me. $\endgroup$ Dec 9, 2014 at 8:04
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    $\begingroup$ @mikuszefski I believe this specific generating function was first published by RJ Riddell in his 1951 dissertation (though he credits Pólya), which I couldn't find online. He and GE Uhlenbeck develop the idea quite well in "On the Theory of the Virial Development of the Equation of State of Monoatomic Gases" (J. Chem. Phys., November 1953). Once you kindly answered my question, I found the paper, and it's now obvious. Thanks again! $\endgroup$ Dec 9, 2014 at 9:37
  • $\begingroup$ Thanks for the paper. Never seen so much formulae in an abstract. Not my topic, but seems to be interesting. $\endgroup$ Dec 9, 2014 at 9:50

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