Stirling

The Stirling number of the second kind : the number of ways to partition an n-set into k non-empty blocks

WikipediaStirling numbers of the second kindMathWorldStirlingNumberoftheSecondKindWikidataQ2601117DLMF26.8.i.p3Fungrim entry9fbe4fOEISA008277Wolfram LanguageStirlingS2✓

Stirling(n, k)the number of partitions of an -set into blocks

SageMathstirling_number2(n, k)SymPystirling(n, k)

Domain: Combinatorics

Details

compute-engine spells the second-kind number as .
It satisfies the recurrence
Summing over gives the Bell number: (see BellNumber)
The signed first-kind numbers are StirlingS1

Examples

See also: StirlingS1, BellNumber, SetPartitions