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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
Get started now by creating a new collection.
Don't knock your approach just yet. I think we're using the same one, and Javascript's precision craps out around n = 43. Your math is probably fine.
I'm going to try in Python to verify.
Edit: Somewhat verified in Python. It works with n = 47, but the python built-in test cases only go to 20, and I'm not willing to build out all the real answers from Wolfram|Alpha to make my own test suite to 200.