OFFSET
1,3
COMMENTS
The trees are unordered (see A000081). For balanced ordered rooted trees see A079500. - Joerg Arndt, Jul 20 2014
The trees are unlabeled. For labeled version see A238372. - Alois P. Heinz, Dec 29 2014
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..3500 (terms 1..300 from Alois P. Heinz)
Joerg Arndt, balanced unordered rooted trees for n = 1..10
EXAMPLE
See Arndt link.
From Gus Wiseman, Oct 08 2018: (Start)
The a(1) = 1 through a(7) = 12 balanced rooted trees with n nodes:
o (o) (oo) (ooo) (oooo) (ooooo) (oooooo)
((o)) ((oo)) ((ooo)) ((oooo)) ((ooooo))
(((o))) (((oo))) (((ooo))) (((oooo)))
((o)(o)) ((o)(oo)) ((o)(ooo))
((((o)))) ((((oo)))) ((oo)(oo))
(((o)(o))) ((((ooo))))
(((((o))))) (((o)(oo)))
((o)(o)(o))
(((((oo)))))
((((o)(o))))
(((o))((o)))
((((((o))))))
(End)
MATHEMATICA
T[n_, k_] := T[n, k] = If[n==1, 1, If[k==0, 0, Sum[Sum[If[d<k, 0, T[d, k-1] * d], {d, Divisors[j]}]*T[n-j, k], {j, 1, n-1}]/(n-1)]]; a[n_] := Sum[ T[n, k], {k, 0, n-1}]; Array[a, 40] (* Jean-François Alcover, Jan 08 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Apr 15 1999
STATUS
approved