Upgrading from:

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}]

CatalanNumber can now be evaluated numerically for noninteger arguments:

Version 5.2 N[CatalanNumber[1/2]] returns unevaluated

CatalanNumber can now be evaluated for complex arguments:

Version 5.2 CatalanNumber[0.5 I] returns unevaluated

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}]

Subfactorial can now be evaluated numerically for noninteger arguments:

Version 5.2 N[Subfactorial[1/2]] returns unevaluated

Subfactorial can now be evaluated for complex arguments:

Version 5.2 Subfactorial[1.5 + I] returns unevaluated

Hofstadter's function

Define Hofstadter's function:

Version 5.2 << DiscreteMath`CombinatorialFunctions`; Hofstadter[100]