cp's OEIS Frontend

A318901 Number of n-node rooted trees in which five equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.

%I A318901 #4 Sep 05 2018 11:41:18
%S A318901 1,1,3,8,22,59,163,450,1254,3505,9846,27740,78412,222175,630993,
%T A318901 1795524,5118371,14613211,41780583,119605948,342793785,983487162,
%U A318901 2824375723,8118198640,23353430828,67230869761,193682427149,558333769713,1610500116245,4648080322122
%N A318901 Number of n-node rooted trees in which five equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.
%H A318901 Alois P. Heinz, <a href="/A318901/b318901.txt">Table of n, a(n) for n = 5..2143</a>
%p A318901 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A318901       `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p A318901     end:
%p A318901 a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(5):
%p A318901 seq(a(n), n=5..35);
%Y A318901 Column k=5 of A255704.
%K A318901 nonn
%O A318901 5,3
%A A318901 _Alois P. Heinz_, Sep 05 2018