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Is there a quick way of checking - either by hand or computationally - whether or not a given integer is a binomial coefficient?

If there isn't, is there a website where one can check this easily?

Hypergeometricx
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    Probably you're ignoring the coefficient ${N\choose 1} = N$, is any solution $N ={n \choose k}$ with $k > 1$ OK? – pjs36 Nov 16 '16 at 16:46
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    @pjs36 - Yes, not just the trivial cases. Not only any but all solutions if possible. – Hypergeometricx Nov 16 '16 at 21:51
  • Just saw this and was reminded of your question. Do you think it's relevant here? – pjs36 Dec 16 '16 at 00:41
  • @pjs36 - Thanks. Looks interesting. Have also come across that conjecture on wiki. It But it does not really allow you to check if a given number is a binomial coefficient. – Hypergeometricx Dec 16 '16 at 04:26

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https://oeis.org/

For example, for ${16\choose 9}= 11440 $ the web site lists it as belonging to binomial coefficient series $C(2n, n-1)$,$C(n,7)$,$C(n,9)$.

As a general question, it looks like an interesting problem and I also could not find any reference to this general topic. However, the easiest way for me was to write a small program that checks if a certain number is a binomial coefficient or not.

Eddward
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