Q:

What is the missing number and the correct sequence?

I have a riddle, you might wanna help solve.

Just imagine, we would like to change the sequence (that works very well now [in German there is the term "funktioniert 1A" - which translates into somewhat like "works optimally" and which could be a clue]) of the following numbers. What could that sequence be?
84474, 349272, 1284192, 6648480, 24948000, 63504000, 97511040, 240166080
Additionally, one number is missing! Please tell me which one and include it into the sequence I'm searching for!

A:

Partial answer:
The second series fits the function
g(x) = (29*x^7 - 694*x^6 + 6560*x^5 - 31150*x^4 + 77711*x^3 - 94876*x^2 + 46740*x + 46080)/720
When you insert the values 0 - 7 for x, then the values of the series are emitted in ascending order, but you write, that the order may be other than given. When inserting the value 8, then the result is 546, which might be the result that you are looking for!

A:

The solution is:

 84474, 240166080, 6648480, 1284192, 63504000, 349272, 5027400, 97511040, 24948000

Explanation:

 Step 1: Perform integer factorization for each number
 Step 2: Convert each integer to a letter 1A (1=A)
 Step 3: Each number corresponds to a "starter" Pokémon
 Step 4: Find the missing one, convert to number
 Step 5: Sort alphabetically

