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Of course, I can use Stirling's approximation, but for me it is quite interesting, that, if we define $k = (n-1)!$, then the left function will be $(nk)!$, and the right one will be $k! k^{n!}$. I don't think that it is a coincidence. It seems, that there should be smarter solution for this, other than Stirling's approximation.

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    You don't think "what" is a coincidence?2012-10-09
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    I cannot explicitely explain why did I say so. Probably, I just wanted to point that it seems that there should be smarter solution others than Stirling's approximation. But, of course, I can be wrong.2012-10-09

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