OFFSET
0,3
COMMENTS
Organic vertex labeling with numbers 1,2,...,n means that the sequence of vertex labels along the (unique) path from the root with label 0 to any leaf (non-root vertex of degree 1) is increasing.
Row lengths sequence, i.e. the number of rooted ordered trees, C(n):=A000108(n) (Catalan numbers): [1,1,2,5,14,42,...].
Number of rooted trees with n non-root vertices [1,1,2,4,9,20,...]=A000081(n+1).
LINKS
EXAMPLE
[0! ]; [1! ]; [2!,1]; [3!,3,3,2,1], [4!,12,12,12,8,8,6,6,4,4,3,3,2,1];...
n=3: 3 labelings (0,1,2)(0,3), (0,1,3) (0,2) and (0,2,3) (0,1) for the rooted tree o-o-x-o.
n=3: 3 labelings (0,3)(0,1,2), (0,2)(0,1,3) and (0,1)(0,2,3) for the rooted tree o-x-o-o.
CROSSREFS
KEYWORD
nonn,more,tabf
AUTHOR
Wolfdieter Lang, Aug 07 2007
STATUS
approved