most recent 30 from http://mathoverflow.net 2013-05-18T18:10:01Z http://mathoverflow.net/feeds/user/12389 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52671/number-of-muti-indices-of-a-fixed-order-which-are-less-than-a-given-multi-index/52790#52790 unknown (google) 2011-01-21T20:37:57Z 2011-01-21T20:37:57Z

<p>The number of solutions to the equation $a_{1}+a_{2}+\cdots+a_{n}=k$ where $s>a_{i}\geq0$, $a_{i}\in\mathbb{N}$ for all i is (unless I typo'd) $\sum_{j=0}^{n}\left(-1\right)^{j}\binom{n}{j}\binom{n+k-js-1}{n-1}$</p>