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Number of partitions with limited cardinality [duplicate]
We are given $k$ urns labeled from $1$ to $k$. What is the number of ways to put $n$ indistinguishable balls into the $k$ (distinct) urns, given that each urn has a limited capacity equal to $c$, ...
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Number of ordered set partitions with subset size $\leq 3$
For $n \ge 0$, let $h_n$ be the number of ways of taking $n$ (distinguishable)
rabbits, putting them into identical cages with one to three rabbits per
cage and then ordering the cages in a row. Find ...