How to simplify infinite multiple?

Question

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 $n!!$?

Thanks

Answer 1

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 $$ sf(n)=\prod^n_{k=1}k!$$

Answer 2

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