I did a sum() on a generator which essentially does the same thing - which reduces LOC but is less clean. I guess OP just wanted to keep the code clean and given the factorial nature of the input, recursion stack won't run out.

Yep, we should't have to rely on test cases to get some rules that weren't clearly stated in description.

recursion is not working at all in this case, the only way is to use mathematical algorithm for this problem

Yeah, the writer of this problem seems to put a space between their words and punctuation marks.
Also, the algorithm that we are being made to implement here is not the algorithm for encoding into pig latin that I was taught (ie: multiple letters need to be shifted to the back until you reach the first vowel)

you will change opinion when you will see that in fact, recursion is the only one way to go with for fast.

old kata == easy kata