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I am desperately searching for a paper I once have read, but cannot find anymore. It was about a counting function f(n) - the only thing I remember is that f's expression contained n! and 2n - and the question in the title was something like "What does f(n) count?". The paper compared three or so different approaches, and was written as a trialog.

Can someone point me to this paper?

If you know about other papers on this question - "What does f(n) count?", with f(n) any counting-but-what function, I'd be happy to learn about them.

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  • $\begingroup$ A negative result: I tried sticking "what does" into the title field at Math Reviews and got many hits but didn't get anything like what you're looking for. $\endgroup$
    – Gerry Myerson
    Commented Sep 13, 2010 at 6:56
  • $\begingroup$ I also searched for "what does" in math titles at the arXiv and found nothing relevant. $\endgroup$
    – Gerry Myerson
    Commented Sep 13, 2010 at 7:02
  • $\begingroup$ Thanks for the endeavor, but that's why I said something like "What does f(n) count?". It also could have been "What's f(n) the number of?" or something like that. $\endgroup$
    – Hans-Peter Stricker
    Commented Sep 13, 2010 at 7:24
  • $\begingroup$ I am afraid you would have to know the paper, because you won't find it by searching. $\endgroup$
    – Hans-Peter Stricker
    Commented Sep 13, 2010 at 7:25
  • $\begingroup$ Fair enough. I was just hoping to save someone else the trouble of going down the one particular blind alley. $\endgroup$
    – Gerry Myerson
    Commented Sep 13, 2010 at 7:25

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Could it be The answer is $2^n·n$! What's the question? by Gary Gordon (Amer. Math. Monthly 106 (1999), no. 7, 636–645)?

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    $\begingroup$ @Hans ...and thank you! I just enjoyed a little Monday morning procrastination skimming this nice paper. $\endgroup$
    – Bob Durrant
    Commented Sep 13, 2010 at 10:07
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    $\begingroup$ In case you don't have JSTOR, here is a free version on author's website: webbox.lafayette.edu/~gordong/pubs/2%5En.pdf $\endgroup$
    – Igor Pak
    Commented Sep 13, 2010 at 13:29
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One question of this kind can be found on MO:

What does the generating function $x/(1 - e^{-x})$ count?

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