Lah number
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In mathematics, Lah numbers, discovered by Ivo Lah in 1955, are coefficients expressing rising factorials in terms of falling factorials.
Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a set of n elements can be partitioned into k nonempty subsets and in such a way that all elements of the same subset are linearly ordered. Lah numbers are related to Stirling numbers.
Unsigned Lah numbers:
Signed Lah numbers
Paraphrasing Karamata-Knuth notation for Stirling numbers it was proposed to use the following alternative notation for Lah numbers:
