Bell number with minimum bound on partition size

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I know that the Bell number $B_n$ is the number of ways to partition a set of $n$ elements into distinct non-empty subsets. Is there a variant of this number that specifies the minimum number of elements in each particular subset? For example, I want to compute the number of partitions of a set of $n$ elements such that each partition contains at least $m$ elements ($m < n$). How can this be done?