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For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.

4 votes

Asymptotic expression for $j$ which satisfies $\binom{n}{j}/j! \sim k$ as $n\to\infty$

This is not quite an answer to the question (Brendan McKay already gave quite a satisfactory one), but it's worth adding that $\binom{n}{j}/j!$ has an interesting probabilistic interpretation, name …
Dan Romik's user avatar
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