cp's OEIS Frontend

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.

%I A318905 #4 Sep 05 2018 12:06:45
%S A318905 1,1,3,8,22,60,167,465,1306,3680,10418,29582,84261,240581,688458,
%T A318905 1973887,5669197,16307404,46973290,135474784,391164385,1130600056,
%U A318905 3270921899,9471289877,27447106048,79598738454,231001452777,670812581033,1949157218646,5666759197092
%N 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.
%H A318905 Alois P. Heinz, <a href="/A318905/b318905.txt">Table of n, a(n) for n = 9..2137</a>
%p A318905 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A318905       `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p A318905     end:
%p A318905 a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(9):
%p A318905 seq(a(n), n=9..39);
%Y A318905 Column k=9 of A255704.
%K A318905 nonn
%O A318905 9,3
%A A318905 _Alois P. Heinz_, Sep 05 2018