I noticed that the following identity for a summation of stars and bars held for specific k but I was wondering if someone could provide a general proof via combinatorics or algebraic manipulation. I wouldn't be surprised if this is a known result; it looks very similar to the Hockey Stick identity.
k∑i=0(d+i−1d−1)=(d+kk)
The left can be immediately rewritten as ∑ki=0(d+i−1i) if it helps inspire intuition.
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