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.

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

Author

Alois P. Heinz, Sep 05 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..2137

Crossrefs

Column k=9 of A255704.

Programs

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);