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[ImplState=stable,TestState=stable,DocState=stable]

combinat::stirling1 -- Stirling numbers of the first kind

Introduction

combinat::stirling1(n,k) computes the Stirling numbers of the first kind.

Call(s)


combinat::stirling1(n,k)

Parameters

n,k- nonnegative integers

Returns

an integer.

Details

Example 1

Let us have a look what's the result of x*(x-1)*(x-2)*(x-3)*(x-4)*(x-5) written as a sum.

>> expand(x*(x-1)*(x-2)*(x-3)*(x-4)*(x-5)) 
                    2                3       4       5    6
               274 x  - 120 x - 225 x  + 85 x  - 15 x  + x

Now let us ``prove'' the formula mentioned in the ``Details'' section by calculating the proper Stirling numbers:

>> combinat::stirling1(6,1); 
   combinat::stirling1(6,2); 
   combinat::stirling1(6,3); 
   combinat::stirling1(6,4); 
   combinat::stirling1(6,5); 
   combinat::stirling1(6,6) 
                                   -120
      
                                    274
      
                                   -225
      
                                    85
      
                                    -15
      
                                     1

Example 2

>> combinat::stirling1(3,-1) 
      Error:  Arguments must be nonnegative integers. [combinat::sti\
      rling1]

Further Documentation

J.J. Rotman, An Introduction to the Theory of Groups, 3rd Edition, Wm. C. Brown Publishers, Dubuque, 1988

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