cp's OEIS Frontend

A318825 Number of rooted trees with n nodes such that ten equals the maximal number of subtrees of the same size extending from the same node.

%I A318825 #4 Sep 04 2018 15:49:36
%S A318825 0,1,1,3,8,22,60,167,465,1306,3681,10423,29598,84313,240753,689013,
%T A318825 1975659,5674795,16324964,47028023,135644560,391688795,1132214229,
%U A318825 3275875477,9486452270,27493411521,79739873360,231430860268,672117013805,1953114161607,5678747123701
%N A318825 Number of rooted trees with n nodes such that ten equals the maximal number of subtrees of the same size extending from the same node.
%H A318825 Alois P. Heinz, <a href="/A318825/b318825.txt">Table of n, a(n) for n = 10..2139</a>
%p A318825 g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318825       binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p A318825     end:
%p A318825 a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(10):
%p A318825 seq(a(n), n=10..40);
%Y A318825 Column k=10 of A318754.
%K A318825 nonn
%O A318825 10,4
%A A318825 _Alois P. Heinz_, Sep 04 2018