The Stirling numbers of the first kind are the coefficients in the expansion
where (a Pochhammer symbol) denotes the falling factorial,
Note that (x)0 = 1 because it is an empty product. Combinatorialists also sometimes use the notation for the falling factorial, and for the rising factorial.
(Confusingly, the Pochhammer symbol that many use for falling factorials is used in special functions for rising factorials.)
The unsigned Stirling numbers of the first kind,
(with a lower-case "s"), count the number of permutations of n elements with k disjoint cycles.
Read more about this topic: Stirling Number
Famous quotes containing the words stirling, numbers and/or kind:
“Oh, if thy pride did not our joys control,
What world of loving wonders shouldst thou see!
For if I saw thee once transformed in me,
Then in thy bosom I would pour my soul;”
—William Alexander, Earl O Stirling (1580?–1640)
“And when all bodies meet
In Lethe to be drowned,
Then only numbers sweet
With endless life are crowned.”
—Robert Herrick (1591–1674)
“Maybe now you, you don’t want to believe it. Maybe you’d like to tell yourself it didn’t happen. But Steve, you’re not the kind of person that can turn your back on something you know is true.”
—Theodore Simonson. Irvin S. Yeaworth, Jr.. Jane Martin (Aneta Corseaut)