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Why it feels like everything is a trade-off

I started tinkering with it before reading the comments but I might as well post my thoughts. My answer was basically the same as Donald Hobson's answer except I pre-calculated the powers and factorials you would use and stored them in an array or collection, then I calculated the sum using the stored values. It's basically the same solution but a little easier to follow. If you aren't worried about breaking taboos then you could stick the factorials in a global variable and have a function to get the factorial that checks to see if the factorial has been calculated and if it hasn't then calculate and store the factorials up to that number. Then again if your hard coded solution works for you then no need to bother adding more complications to it.