A Tree with a special node called the ``Root'' or ``Eve.'' Denote the number of rooted trees with nodes by , then the Generating Function is

(1) |

(2) | |||

(3) |

where is the Generating Function for unrooted Trees. A Generating Function for can be written using a product involving

(4) |

The number of rooted trees can also be calculated from the Recurrence Relation

(5) |

**References**

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/otter/otter.html

Ruskey, F. ``Information on Rooted Trees.'' http://sue.csc.uvic.ca/~cos/inf/tree/RootedTree.html.

Sloane, N. J. A. Sequence
A000081/M1180
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

1999-05-25