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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.
2

%I #4 Sep 05 2018 11:47:04

%S 1,1,3,8,22,60,166,461,1291,3629,10246,29020,82448,234818,670288,

%T 1917054,5492422,15760308,45286760,130293687,375293797,1082109082,

%U 3123088057,9021467714,26080762653,75454838291,218451043430,632849337956,1834453919208,5320549626803

%N 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 Alois P. Heinz, <a href="/A318902/b318902.txt">Table of n, a(n) for n = 6..2138</a>

%p g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-

%p `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)

%p end:

%p a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(6):

%p seq(a(n), n=6..36);

%Y Column k=6 of A255704.

%K nonn

%O 6,3

%A _Alois P. Heinz_, Sep 05 2018