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Dobinski's formula : ウィキペディア英語版 | Dobinski's formula In combinatorial mathematics, Dobiński’s formula〔G. Dobiński, "Summirung der Reihe für ''m'' = 1, 2, 3, 4, 5, …", ''Grunert's Archiv'', volume 61, 1877, pages 333–336 (Internet Archive: ()).〕 states that the ''n''-th Bell number ''B''''n'' (i.e., the number of partitions of a set of size ''n'') equals : The formula is named after G. Dobiński, who published it in 1877. ==Probabilistic content==
In the probability theory setting, Dobinski's formula represents the ''n''th moment of the Poisson distribution with expected value 1. Sometimes Dobinski's formula is stated as the number of partitions of a set of size ''n'' equals the ''n''th moment of that distribution.
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