The last post in this sequence was about some more general way to work with the prime factorization of the factorials and about the Narayana numbers:
Which expands to
Using and vice versa we can shove more things together and get
Get the non-factorials out of the way
With the prime factorization of and with their arithmetic resembling the relation of the arithmetic of numbers and the arithmetic of their logarithms (e.g.: ) we get (dropping the fraction with the non-factorials)
We have to be carefull with the term for it can overflow, so we should divide the prime factorization by and by instead of multiplying out and divide by that all together.
The actual implementation is left as an exercise for the reader.
Or just wait until I do it myself in the next days 😉