olymmath

HMMT 2016 U6

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Consider a 2×n2 \times n grid of points and a path consisting of 2n−12 n-1 straight line segments connecting all these 2n2 n points, starting from the bottom left corner and ending at the upper right corner. Such a path is called efficient if each point is only passed through once and no two line segments intersect. How many efficient paths are there when n=2016n=2016 ?

Dataset text NuminaMath olympiads. Quoted with source.

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\binom{4030}{2015}

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