Weighted trees

[franktaw at netscape.net]

Thanks for the very nice calculation.  I have now submitted the cases k = 0 and k = 1 to the OEIS, giving you credit.
 
I described my original sequence using the phrase "rooted trees" in the name line.  Once  it has been established what kind of trees one is talking about, I don't really think it is necessary to include the entire description on each subsequent repetition.
 
Franklin T. Adams-Watters
 
 
-----Original Message-----
From: Christian G. Bower bowerc at usa.net


...
Let a<k>(n) be the number of rooted trees taking root to be level k.

Then a<k>(n) is Euler transform of a<k+1>(n) shifted right k places.

Let us take a<k>(n) to be the sequence with a<k>(k) = 1 and all other 0.
...

PS

If you'll excuse my retentiveness, it would be nice to call
trees: trees and rooted trees: rooted trees since both are in the
EIS in abundance and they are not the same thing.
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