Define <n,k> := number of ways to throw n distinct (numbered) balls
into k distinct (numbered) non-empty bins [there must be at least one
ball in each bin. the order of the balls within each bin is immaterial.]
It is easy to see that
<n,0> = Kronecker_delta(n,0),
and we also have the recurrence relation
<n+1,k> = k(<n,k> + <n,k-1>)
what are these numbers <n,k>?
Stirling Numbers of the 4th Kind?
How are they related to the other kinds of Stirling Numbers?
any literature on this kind of numbers?