A318906 - OEIS

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 #4 Sep 05 2018 12:15:39

%S 1,1,3,8,22,60,167,465,1306,3681,10421,29593,84298,240705,688859,

%T 1975176,5673279,16320250,47013406,135599456,391550002,1131788538,

%U 3274572887,9482475518,27481293566,79703012121,231318904534,671777453618,1952085567096,5675634863875

%N 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 Alois P. Heinz, <a href="/A318906/b318906.txt">Table of n, a(n) for n = 10..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))(10):

%p seq(a(n), n=10..40);

%Y Column k=10 of A255704.

%K nonn

%O 10,3

%A _Alois P. Heinz_, Sep 05 2018