Function Repository Resource:

# LahL

Evaluate the Lah number

Contributed by: Jan Mangaldan
 ResourceFunction["LahL"][n,m] gives the Lah number L(n,m).

## Details

Integer mathematical function, suitable for both symbolic and numerical manipulation.
L(n,m) gives the number of ways of partitioning a set of n elements into m non-empty linearly ordered subsets.
ResourceFunction["LahL"] automatically threads over lists.

## Examples

### Basic Examples (1)

Evaluate some Lah numbers:

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### Scope (1)

LahL threads elementwise over lists:

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### Applications (3)

Plot Lah numbers on a logarithmic scale:

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Express Pochhammer as a linear combination of FactorialPower:

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Express FactorialPower as a linear combination of Pochhammer:

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Closed form of derivatives of 1/x:

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### Properties and Relations (3)

Generate values from the generating function:

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Lah numbers can be expressed in terms of Stirling numbers of both kinds:

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Lah numbers are given by a partial Bell polynomial with factorial arguments:

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## Version History

• 1.0.0 – 17 May 2021