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Stirling2

computes the Stirling numbers of the second kind

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Stirling2(n, m)

combinat[stirling2](n, m)

Parameters

n, m

-

integers

Description

• 

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!−1km

  

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.

Examples

Stirling2 only evaluates to a number when m and n are positive integers

Stirling2n,m

Stirling2n,m

(1)

=convert,Sum

Stirling2n,m=_k1=0mbinomialm,_k1_k1nm!1m+_k1

(2)

eval,n=10,m=5

42525=_k1=051120binomial5,_k1_k11015+_k1

(3)

value

42525=42525

(4)

See Also

combinat

Stirling1

 


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