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Just to sharpen my intuition in combinatorics, I ask you of ways to think about interesting combinatorical quantities and expressions like the binomial coefficient, for example, for the binomial coefficient I know the following

  • There are $\binom{n}{k}$ ways to choose k elements from a set of n elements
  • There are $\binom{n}{k}$ strings over $\{0,1\}$ with exactly $k$ ones
  • There are $\binom n k$ shortest paths in an rectangular grid from $(0,0)$ to $(k, n-k)$.

Are there more?

  • 7
    http://oeis.org/A0073182012-07-17

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