BellNumber

The nth Bell number, counting the ways to partition a set of n elements.

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BellNumber(n)the nth Bell number , the number of partitions of an n-element set.

SageMathbell_number(n)SymPybell(n)

Domain: Combinatorics

Details

Recurrence , built from Binomial and the lower Bell numbers.
Generating function .
Equals the sum of Stirling numbers of the second kind over all block counts, .
Also arise as the nth moment of a Poisson distribution with mean 1.
compute-engine requires a nonnegative integer argument; a negative n is left unevaluated.

Examples

See also: StirlingS1