cp's OEIS Frontend

A318904 Number of n-node rooted trees in which eight equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.

%I A318904 #4 Sep 05 2018 12:00:05
%S A318904 1,1,3,8,22,60,167,465,1305,3677,10407,29545,84137,240180,687169,
%T A318904 1969805,5656352,16267296,46848655,135089324,389976522,1126951399,
%U A318904 3259744738,9437132452,27342937037,79281644947,230037790501,667888276997,1940294941620,5639933760363
%N A318904 Number of n-node rooted trees in which eight equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.
%H A318904 Alois P. Heinz, <a href="/A318904/b318904.txt">Table of n, a(n) for n = 8..2137</a>
%p A318904 g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
%p A318904       `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
%p A318904     end:
%p A318904 a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(8):
%p A318904 seq(a(n), n=8..38);
%Y A318904 Column k=8 of A255704.
%K A318904 nonn
%O A318904 8,3
%A A318904 _Alois P. Heinz_, Sep 05 2018