[math-fun] Inverse factorial?

Suppose you place N things in N buckets. How many do expect the fullest bucket to contain? I know that the number of buckets containing k things, on average, is N/(k! e). So I can pretend to get the fullest bucket by setting this equal to 1 and solving for k: you expect around one bucket with "(N/e) un-factorial" items. (Surely this function has a name?) Any recommendations on a smarter approach? --Michael -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.