An example:
The sum $\displaystyle = \sum_{k=1}^n k$
Therefore, the set $= \{1,...,n\}$.
In this particular case, one could of course just use $\Bbb N^n$, but in other cases, this would not be the case. So, what kind of notation can give you an ordered set containing the summands/factors in a sum/product, with the order given by the indexation.
The set containing all the summands of $\sum_{k=1}^n a_k$ is given by $\{ a_k | 1\leq k \leq n\}$.
We don't speak of "ordered sets" in math. If you want something like an ordered set then you are likely looking for a tuple. As for the tuple containing all summands of $\sum_{k=1}^n a_k$, this tuple could be identified with the function $f:\{1,2,\ldots,n\}\to\mathbb{R}$ given by $f(k) = a_k$. In other words, this is just the finite sequence $(a_k)_{k=1}^n$.