Central binomial coefficients

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A central binomial coefficient is a binomial coefficient of the form ${\binom {2n}{n}}$. They are "central" because they appear in the center column of Pascal's triangle. See A000984.

The central binomial coefficients can also be computed as

$\sum _{k=0}^{n}{\binom {n+k-1}{k}}$

or

${\frac {2^{n}}{n!}}\prod _{k=0}^{n-1}2k+1$.