However, you can do much better, exploiting overlap, using only 93,884,313,611 episodes, which is really quite remarkable, because it is just 1.08 episodes per permutation.
Example with 3 (from the article):
3! = 6 permutations
Bad way to watch all: concatenate all permutations
A) 123 132 213 231 312 321 (= 3*6 = 18 episodes, or 3 episodes per permutation)
Good way to watch all permutations:
B) 123121321 (= 9 episodes, or 1.5 episodes per permutation)
Note that each of the permutations above in A is contained in the string at B).
The lower bound is achieved when the permutations overlap perfectly, e.g. when n = 2:
1, 2, 1
The upper bound is simply the concatenation of all permutations. You can get lower than this by exploiting the fact that some permutations' suffixes are other permutations' prefixes.