It seems that your confusion here is with the presentation of the formula; so, let me give you a slightly different description. Perhaps that description will make the notation you used make more sense.

For $n\in\mathbb{N}$, we define $n!$ to be the product of all natural numbers between $1$ and $n$, inclusive: that is, $$ n!=\prod_{i=1}^{n}i=1\cdot2\cdot3\cdots\cdot(n-1)\cdot n. $$ The "$\cdots$" notation takes a bit of getting used to; it is basically intended to mean "and so on" or "continuing in this way". It expresses that there's a pattern at work, and that the pattern continues on in the obvious way. The first few terms are used to establish the pattern, and the final terms describe where the pattern stops.