Stirling2
computes the Stirling numbers of the second kind
Calling Sequence
Parameters
Description
Examples
Stirling2(n, m)
combinat[stirling2](n, m)
n, m
-
integers
The Stirling2(n,m) command computes the Stirling numbers of the second kind from the well-known formula in terms of the binomial coefficients.
Stirling2n,m=∑k=0mmkknm!−1k−m
Instead of Stirling2 you can also use the synonym combinat[stirling2].
Regarding combinatorial functions, Stirling2n,m is the number of ways of partitioning a set of n elements into m non-empty subsets. The Stirling numbers also enter binomial series, Mathieu function formulas, and are relevant in applications in Physics.
Stirling2 only evaluates to a number when m and n are positive integers
Stirling2n,m
=convert,Sum
Stirling2n,m=∑_k1=0mm_k1_k1nm!−1−m+_k1
eval,n=10,m=5
42525=∑_k1=055_k1_k110120−1−5+_k1
value
42525=42525
See Also
combinat
Stirling1
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