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A318902 Number of n-node rooted trees in which six equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.

%I A318902 #4 Sep 05 2018 11:47:04
%S A318902 1,1,3,8,22,60,166,461,1291,3629,10246,29020,82448,234818,670288,
%T A318902 1917054,5492422,15760308,45286760,130293687,375293797,1082109082,
%U A318902 3123088057,9021467714,26080762653,75454838291,218451043430,632849337956,1834453919208,5320549626803
%N A318902 Number of n-node rooted trees in which six equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.
%H A318902 Alois P. Heinz, <a href="/A318902/b318902.txt">Table of n, a(n) for n = 6..2138</a>
%p A318902 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A318902       `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p A318902     end:
%p A318902 a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(6):
%p A318902 seq(a(n), n=6..36);
%Y A318902 Column k=6 of A255704.
%K A318902 nonn
%O A318902 6,3
%A A318902 _Alois P. Heinz_, Sep 05 2018