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Is there any easy characterisation for the numbers which appear in Pascal's triangle that ARE NOT $\dbinom{n}{1}$, $\dbinom{n}{n-1}$?

Is there a fast way to determine if some number (given its prime factorisation) appears in the described manner?

Thanks!!!!!

extremeaxe5
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    Just look here: http://oeis.org/A006987. – Dietrich Burde Sep 08 '14 at 14:26
  • The following characterization of your problem might be more evocative to the reader: Which numbers appear at least three elements deep into Pascal's triangle? (Those which are one element deep are all equal to $1=\binom{1}{1}$, and those which are two elements deep are of the form you give.) – Semiclassical Sep 08 '14 at 14:29

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