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I think that this question of whether or not it's homework is a red herring. The question as written led one to believe that the OP knew the answer and was asking us to find a proof. I don't think such questions are appropriate in MO. The question, as it turns out, is interesting and certainly I'd like to see David's answer attached to it. However it would take some rewriting of the question for me to vote to reopen.
The criterion that there shouldn't be questions on MO to which the answer is well-known doesn't quite seem the right one to me (although I can see that it works in many cases). For example at about the same time, another question was asked: http://mathoverflow.net/questions/44608/do-the-standard-conjectures-imply-parts-of-the-weil-ii-riemann-hypothesis
and I am sure no one will argue that this is not appropriate, by virtue of asking for a proof of something that is already known. It seems tricky to draw the right line.
(I remember being given this question as a sort of a cruel exercise in first year calculus. I'm still not sure whether or not it was a moral thing to do, the instructor obviously knowing it is an open problem, or at least a problem not accessible to us.. )
Anyway, it's understandable at first sight it seemed like homework. I do think though that as soon as people realized it couldn't be homework (because it's too difficult) and that the only problem is the phrasing, any of you guys with enough reputation shouldn't have hesitated to quickly edit it (just a few word changes) and re-opened, as there is real mathematical content to discuss here, as seen in math.stackexchange.
I would probably have voted to close on the basis of it being pretty unmotivated and the flavour of the question is that the person asking it is not particularly skilled mathematically. At the kind of level of person I expect on MO, I would have at least expected the questioner to have gotten to the point about it depending on how n!/2pi goes.
I would prefer questions like this to start on math.SX and then migrate here if someone there says: "This is hard (because XYZ) and I recommend asking it on MO to see if anyone there has any better ideas.". Then, in the second asking, the sticky point can be brought to the fore and made the focus of the question (retaining the original as motivation).
So now that David has answered on math.SX, then this question on MO in its current form should not be reopened. It could be reopened as a follow-up question to David's answer to see if anyone has anything more to add, but it would need extensive rewriting to do that.
The next level after: "Good answers do not make good questions" is "Good questions do not make good MO questions". Namely, if I ask a question in algebraic geometry that just happens to be a really good question but I have not the wit to understand that then it's not a good MO question.
I see that it has now been reopened.
I would like to know if the questioner has any further interest in this question, given the answer at math.SX.