StirlingS1

The signed Stirling number of the first kind, relating falling factorials to powers of n.

WikipediaStirling numbers of the first kindMathWorldStirlingNumberoftheFirstKindWikidataQ2657556DLMF26.8.i.p1FungrimStirlingS1Fungrim entry071a9418ec99OEISA008275Wolfram LanguageStirlingS1✓

StirlingS1(n, k)the signed Stirling number of the first kind .

SageMathstirling_number1(n, k)

Domain: Combinatorics

Details

Coefficients relating falling factorials to ordinary powers: .
counts the permutations of n elements with exactly k cycles.
and for , with the boundary case .
The unsigned values in each row sum to :
.
compute-engine's StirlingS1 is scalar-only; it does not thread the first argument over a list.

Examples

See also: Binomial, Stirling