Vandermonde's identity

$ \sum_{i=0}^k \binom{n}{i}\binom{m}{k - i} = \binom{n+m}{k}

[Number of routes

https://gyazo.com/623501bda4290cb7ffb28196502933b5

special case(k=n, m=n)

$ \sum_{i=0}^n \binom{n}{i}^2 = \binom{2n}{n}

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