cp's OEIS Frontend

A318823 Number of rooted trees with n nodes such that eight equals the maximal number of subtrees of the same size extending from the same node.

%I A318823 #4 Sep 04 2018 15:06:19
%S A318823 0,1,1,3,8,22,60,167,465,1307,3682,10422,29593,84291,240663,688685,
%T A318823 1974519,5670976,16312405,46987424,135514856,391278424,1130925409,
%U A318823 3271852293,9473955776,27454758665,79620740071,231064799358,670995202298,1949684311164,5668282144436
%N A318823 Number of rooted trees with n nodes such that eight equals the maximal number of subtrees of the same size extending from the same node.
%H A318823 Alois P. Heinz, <a href="/A318823/b318823.txt">Table of n, a(n) for n = 8..2137</a>
%p A318823 g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318823       binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p A318823     end:
%p A318823 a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(8):
%p A318823 seq(a(n), n=8..38);
%Y A318823 Column k=8 of A318754.
%K A318823 nonn
%O A318823 8,4
%A A318823 _Alois P. Heinz_, Sep 04 2018