Bell numbers

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The Bell numbers are given by

or by


where are Stirling numbers (cf. Combinatorial analysis) of the second kind, so that is the total number of partitions of an -set.

They are equal to .

The name honours E.T. Bell.


[a1] L. Comtet, "Advanced combinatorics" , Reidel (1974)
How to Cite This Entry:
Bell numbers. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by N.J.A. Sloane (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article