The double factorial is a generalization of the usual Factorial defined by

(1) |

There are many identities relating double factorials to Factorials. Since

(2) |

(3) |

it follows that . Since

(4) |

(5) |

(6) |

(7) |

For Even,

(8) |

Therefore, for any ,

(9) |

(10) |

The double factorial is a special case of the Multifactorial.

**References**

Sloane, N. J. A. Sequence
A006882/M0876
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-24