A318899 - OEIS

A318899

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

%I #5 Sep 05 2018 11:15:54

%S 1,1,3,7,18,45,116,298,776,2025,5322,14030,37155,98685,262961,702497,

%T 1881475,5050140,13583622,36605565,98821445,267220361,723704046,

%U 1962830775,5330900916,14497096134,39472561082,107601053713,293643574776,802203904616,2193758306687

%N Number of n-node rooted trees in which three 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="/A318899/b318899.txt">Table of n, a(n) for n = 3..2209</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))(3):

%p seq(a(n), n=3..35);

%Y Column k=3 of A255704.

%K nonn

%O 3,3

%A _Alois P. Heinz_, Sep 05 2018