[seqfan] Number of Trees
Jim Nastos
nastos at gmail.com
Fri Mar 6 21:10:50 CET 2009
The following message refers to the sequences:
http://www.research.att.com/~njas/sequences/A000055
http://www.research.att.com/~njas/sequences/A000081
A000055 is the number of trees on n nodes (connected, unlabeled).
There is Maple code given on that page as follows:
b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1,
k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember;
add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember;
unapply (add (b(k)*x^k, k=1..n), x) end: a:= n-> coeff (series (1+
B(n)(x)- (B(n)(x))^2/2+ B(n)(x^2)/2, x=0, n+1), x, n): seq (a(n),
n=0..32); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21
2008]
This code does not generate A000055 but instead generates the sequence
A000081, which is the number of rooted trees on n nodes.
A000081 already has plenty of code available, so I suggest the above
code is removed from A000055.
Also, the b-file for A000055 has the first 200 terms ... can anyone
whip up the first 1000 terms?
JN
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