HMMT November 2016 U18

An 8 by 8 grid of numbers obeys the following pattern:

The first row and first column consist of all 1 s .
The entry in the $i$ th row and $j$ th column equals the sum of the numbers in the $(i-1)$ by $(j-1)$ sub-grid with row less than $i$ and column less than $j$ . What is the number in the 8 th row and 8 th column?

Dataset text NuminaMath olympiads. Quoted with source.

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2508

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