On Bell numbers of type D
Abstract
In this paper, we will introduce Bell numbers D(n) of type D as an analogue to the classical Bell numbers related to all the partitions of the set [n]. Then based on a signed set partition of type D, we will construct the recurrence relations of Bell numbers D(n). In addition, we deduce the exponential generating function for D(n). Finally, we will provide an explicit formula for D(n).
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