I have a series like

$$1!2!3! ... n!$$

for some finite n. How do I write this in notation? Similar to summation I guess or if it can simply be reduced down to something in terms of n that would be better. Is it $n!!$?



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  • 1
    $\begingroup$ The title is in contradiction with the body of the question. Moreover, $n!!$ is called double factorial and is a totally different thing. I don't think there's a specific notation for your case. $\endgroup$ – rubik Nov 23 '15 at 19:33
  • 1
    $\begingroup$ $\prod_{r=1}^{n}r!$ and $\sum_{r=1}^{n}r!$ $\endgroup$ – Gune Nov 23 '15 at 19:35
  • $\begingroup$ How is that an infinite multiple? $\endgroup$ – Thomas Andrews Nov 23 '15 at 19:44
  • $\begingroup$ It can be written as $\prod_{r=1}^n r^{n-r}$ $\endgroup$ – kingW3 Nov 23 '15 at 20:08

Well i can only assume what you are looking for. By the term in your question i think you might mean a superfactorial. See this Wikipedia Article on Factorials - it might help.

If you mean a product of factorials it would be a notation like $$ sf(n)=\prod^n_{k=1}k!$$


$n!!$ often denotes the semi-factorial, i.e. the product of every other integer up to $n$.


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