HMMT November 2013 E10

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How many functions $f:\{1,2, \ldots, 2013\} \rightarrow\{1,2, \ldots, 2013\}$ satisfy $f(j)<f(i)+j-i$ for all integers $i, j$ such that $1 \leq i<j \leq 2013 ?$

Dataset text NuminaMath olympiads. Quoted with source.

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\binom{4025}{2013}

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