MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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
up vote 10 down vote accepted

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)?

share|cite|improve this answer
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: – Igor Pak Sep 13 '10 at 13:29

One question of this kind can be found on MO:

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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.