DiscreteMath`CombinatorialFunctions`
CatalanNumber and Subfactorial have been added to the built-in Mathematica kernel.
CatalanNumber and Subfactorial can now be evaluated numerically for noninteger arguments.
Subfactorial now accepts complex arguments.
CatalanNumber
Syntax for CatalanNumber is the same as in DiscreteMath`CombinatorialFunctions` in Version 5.2:
Version 5.2
![<< DiscreteMath`CombinatorialFunctions`;
Table[CatalanNumber[n], {n, 1, 10}]](Files/CombinatorialFunctions.en/legacy_1.gif)
CatalanNumber can now be evaluated numerically for noninteger arguments:
Version 5.2
returns unevaluated
![N[CatalanNumber[1/2]]](Files/CombinatorialFunctions.en/legacy_2.gif)
CatalanNumber can now be evaluated for complex arguments:
Version 5.2
returns unevaluated
![CatalanNumber[0.5 I]](Files/CombinatorialFunctions.en/legacy_3.gif)
Subfactorial
Syntax for Subfactorial is the same as in DiscreteMath`CombinatorialFunctions` in Version 5.2:
Version 5.2
![<< DiscreteMath`CombinatorialFunctions`;
Table[Subfactorial[n], {n, 10}]](Files/CombinatorialFunctions.en/legacy_4.gif)
Subfactorial can now be evaluated numerically for noninteger arguments:
Version 5.2
returns unevaluated
![N[Subfactorial[1/2]]](Files/CombinatorialFunctions.en/legacy_5.gif)
Subfactorial can now be evaluated for complex arguments:
Version 5.2
returns unevaluated
![Subfactorial[1.5 + I]](Files/CombinatorialFunctions.en/legacy_6.gif)
Hofstadter's function
Version 5.2
![<< DiscreteMath`CombinatorialFunctions`;
Hofstadter[100]](Files/CombinatorialFunctions.en/legacy_7.gif)