cp's OEIS Frontend

A318906 Number of n-node rooted trees in which ten equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.

%I A318906 #4 Sep 05 2018 12:15:39
%S A318906 1,1,3,8,22,60,167,465,1306,3681,10421,29593,84298,240705,688859,
%T A318906 1975176,5673279,16320250,47013406,135599456,391550002,1131788538,
%U A318906 3274572887,9482475518,27481293566,79703012121,231318904534,671777453618,1952085567096,5675634863875
%N A318906 Number of n-node rooted trees in which ten equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.
%H A318906 Alois P. Heinz, <a href="/A318906/b318906.txt">Table of n, a(n) for n = 10..2138</a>
%p A318906 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A318906       `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p A318906     end:
%p A318906 a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(10):
%p A318906 seq(a(n), n=10..40);
%Y A318906 Column k=10 of A255704.
%K A318906 nonn
%O A318906 10,3
%A A318906 _Alois P. Heinz_, Sep 05 2018