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Stirling's Triangles


	Displays Stirling numbers of the first and second kind for up to ten columns.


	Contributed by: George Beck

Ignoring signs, Stirling numbers of the first kind

count the number of permutations of

that have

cycles.

Stirling numbers of the second kind

count the number of ways the set

can be partitioned into an unordered family of

nonempty subsets. The sums of the

columns are the Bell numbers

, which count the number of set partitions of a set of

elements.

It is remarkable that the two types of triangles are inverses of each other as infinite triangular matrices.

Stirling numbers of the first kind satisfy the recurrence

, while those of the second kind satisfy the very similar

. The recurrences are also similar to the simpler recurrence formula for the binomial coefficients,

Contributed by: George Beck

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