# “What does f(n) count?” - in search for a paper

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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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. –  Gerry Myerson Sep 13 '10 at 6:56
I also searched for "what does" in math titles at the arXiv and found nothing relevant. –  Gerry Myerson Sep 13 '10 at 7:02
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. –  Hans Stricker Sep 13 '10 at 7:24
I am afraid you would have to know the paper, because you won't find it by searching. –  Hans Stricker Sep 13 '10 at 7:25
Fair enough. I was just hoping to save someone else the trouble of going down the one particular blind alley. –  Gerry Myerson Sep 13 '10 at 7:25

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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That's it! Thank you very much!! –  Hans Stricker Sep 13 '10 at 9:42
@Hans ...and thank you! I just enjoyed a little Monday morning procrastination skimming this nice paper. –  Bob Durrant Sep 13 '10 at 10:07
In case you don't have JSTOR, here is a free version on author's website: webbox.lafayette.edu/~gordong/pubs/2%5En.pdf –  Igor Pak Sep 13 '10 at 13:29
What does the generating function $x/(1 - e^{-x})$ count?