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computing terms of polynomial

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hi, I want to compute the number of distinct terms of a M order polynomial and with N inputs by expanding the following: (x_1 + x_2 + x_3 + ... + x_N) ^ M I feel sure there is a formula for computing this but I can't for the life find out or derive what it is. thanks for any help

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Pick some simple values for N and M and see what you get. At some point you'll see a pattern and you can formulate a conjecture.

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