|
|
A318905
|
|
Number of n-node rooted trees in which nine equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.
|
|
2
|
|
|
1, 1, 3, 8, 22, 60, 167, 465, 1306, 3680, 10418, 29582, 84261, 240581, 688458, 1973887, 5669197, 16307404, 46973290, 135474784, 391164385, 1130600056, 3270921899, 9471289877, 27447106048, 79598738454, 231001452777, 670812581033, 1949157218646, 5666759197092
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
9,3
|
|
LINKS
|
|
|
MAPLE
|
g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
`if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
end:
a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(9):
seq(a(n), n=9..39);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|