cp's OEIS Frontend

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 A318899 #5 Sep 05 2018 11:15:54
%S A318899 1,1,3,7,18,45,116,298,776,2025,5322,14030,37155,98685,262961,702497,
%T A318899 1881475,5050140,13583622,36605565,98821445,267220361,723704046,
%U A318899 1962830775,5330900916,14497096134,39472561082,107601053713,293643574776,802203904616,2193758306687
%N 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.
%H A318899 Alois P. Heinz, <a href="/A318899/b318899.txt">Table of n, a(n) for n = 3..2209</a>
%p A318899 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A318899       `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p A318899     end:
%p A318899 a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(3):
%p A318899 seq(a(n), n=3..35);
%Y A318899 Column k=3 of A255704.
%K A318899 nonn
%O A318899 3,3
%A A318899 _Alois P. Heinz_, Sep 05 2018