One can write more compactly $$\sum_{\substack{0\le m_1<n\\0\le m_2<m_1\\\vdots\\0\le m_{n-2}<m_{n-3}\\0\le m_{n-1}<m_{n-2}}}m_{n-1}.$$ Personally, I would first define a set $$S=\{(m_1,\dots,m_{n-1})\in\mathbb N^{n-1}:n>m_1>m_2>\dots>m_{n-2}>m_{n-1}\ge0\}$$ and then write $$\sum_{(m_1,\dots,m_{n-1})\in S}m_{n-1}.$$
↧
