Question: (a) For n 0, let Bn denote the number of partitions of {1, 2, 3, . . . , n}. Set B0 = 1

(a) For n ‰¥ 0, let Bn denote the number of partitions of {1, 2, 3, . . . , n}. Set B0 = 1 for the partitions of 0. Verify that for all n ‰¥ 0,

[The numbers B1,i ‰¥ 0, are referred to as the Bell numbers after Eric Temple Bell (1883-1960).]
(b) How are the Bell numbers related to the Stirling numbers of the second kind?

n+1

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