STIRLING1 _ _ _ _ _ _ _ _ _ _ _ _ operator

The Stirling1 operator returns the Stirling Numbers S(n,m) of the first kind, i.e. the number of permutations of n symbols which have exactly m cycles (divided by (-1)**(n-m)).

syntax:

examples:

Stirling1 (17,4); 

  -87077748875904 


Stirling1 (n,n-1); 

  -gamma(n+1)
  -------------
  2*gamma(n-1)

The operator Stirling1 evaluates the Stirling numbers of the first kind by rulesets for special cases or by a computing the closed form, which is a series involving the operators BINOMIAL and STIRLING2.