Rooted Tree
A Tree with a special node called the ``Root'' or ``Eve.'' Denote the number ofrooted trees with 
nodes by 
, then the Generating Function is
 | |
 | (1) |
 |  |  | (2) |
 | |  | (3) |
where
is the Generating Function for unrooted Trees. A Generating Functionfor can be written using a product involving the sequence itself as | (4) |
The number of rooted trees can also be calculated from the Recurrence Relation
 | (5) |
and 
, where the second sum is over all 
which Divide 
(Finch).See also Ordered Tree, Red-Black Tree, Weakly Binary Tree
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. SequenceA000081/M1180in ``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.
- Combination Lock
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