How do you notate recursive summation?

Question

I have devised the following expression and was just wondering if there is some way to better notate it mathematically.

$$ \sum_{i=0}^{n} \Bigg( \sum_{j=i}^{n} \bigg( \sum_{k=j}^{n} \cdots \sum_{z=y}^{n} (n-z+1) \bigg) \Bigg) $$

where the total number of sigmas is given by $n-1$ .

Answer 1

Maybe $$\sum_{(i,j,\ldots,z)\atop 0\le i\le j\le\ldots\le z\le n}(n-z+1) $$