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  "body": "\n## Definition\n\nLet $n$ be a natural number.\nThe $n$-th central binomial coefficient is the [[binomial coefficient|092GEF38YD]]\n$$\\binom{2n}{n} = \\frac{(2n)!}{(n!)^2}.$$\n\n## Remarks\n\nThe first values, for $n = 0, 1, 2, 3, 4$, are $1, 2, 6, 20, 70$.\nIt is the middle entry of row $2n$ of [[Pascal's triangle|05DME4TZ3K]], and the largest entry of that row.\nIt counts the [[lattice paths|040WY0TT2G]] from $(0, 0)$ to $(n, n)$ with unit steps right and up. The [[closed formula for Catalan numbers|0NNDQVJ54Q]] divides it by $n + 1$.\n\n## Explanations\n\n### L1 human\n\nThe central binomial coefficient is the number in the middle of an even row of Pascal's triangle.\nFor $n = 2$ it is $\\binom{4}{2} = 6$: the ways to choose 2 of 4 objects.\n",
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