Extended Pascal's Triangle Identity -General identity.

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Hello I'm having trouble understanding the following notation, specifically, what "i" is indexing in the summation sign and where does the value of "k" come from? Does the value of "k" come from an arbitrary choice of "k" then the index runs from 0 to that choice ?

$$C(n,r)=\sum_{i=0}^k C(n-k,r-k-i) C(k,i) $$

thanks.