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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
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
Column k=9 of A255704.
Sequence in context: A318902 A318903 A318904 * A318906 A255705 A318867
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 05 2018
STATUS
approved