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I don't know how i can calculate this complicated multivariate sum : $$ S(l,k)=\sum_{|m|=k} s_{l,m}=\sum_{|m|=k} l(l-1)(l-2)\dots(l-m+1) $$ Where $m=(m_1,\dots,m_n)$, $l=(l_1,\dots,l_n)$, and $k$ a non-negative integer and $|m|=m_1+\dots+m_n$. when a term of this sum is explicitly for a $m=(m_1,\dots,m_n)$ such that $\sum_{i=1}^n |m_i|=k$ : $$ s_{l,m}=\prod_{j=1}^{n}l_j \times\prod_{j=1}^{n}(l_j-1)\times\dots\times \prod_{j=1}^{n}(l_j-m_j+1) $$

Hamza
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    Hi! Is this a question about Mathematica or math in general? – Yves Klett Oct 18 '14 at 18:29
  • Hi @Hamza, welcome to Mathematica.SE, please consider taking the tour so you learn the basic rules of the site. Your question may be put on-hold because it seems to be off-topic, ie its about mathematics and not Mathematica. If that's not the case, please edit your question to make it explicitly about Mathematica programming. Include a minimum example of the code you are working on. –  Oct 18 '14 at 19:14
  • Hi, my problem is how i can calculate a such sum with Mathematica, i mean that how i can calculate a multivariate sum with such condition ? – Hamza Oct 19 '14 at 00:34

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