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for questions about multinomial coefficients

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Upper bound for the crossed-terms of a sum of multinomial coefficients

I am trying to upper bound the variance of a centered tree and I would like to get an upper bound which would look like : $$\sum\limits_{\substack{ (l_1, ..., l_d) \neq (k_1, ..., k_d), \\ \sum_{j=1}^ …
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