Probability of matching birthdays (k or more out of N people)

This calculates the probability that at least k people out of N have the same birthday. It is well known that the probability of two people out of N having the same birthday is high, but it drops sharply when the number rises to three, four, and so on.
The calculation formula uses the approximation formula also employed by the R functions `pbirthday` and `qbirthday`:
Diaconis, P. and Mosteller, F. “Methods for studying coincidences.” J. American Statistical Association.
This formula is used here.