cp's OEIS Frontend

A318818 Number of rooted trees with n nodes such that three equals the maximal number of subtrees of the same size extending from the same node.

%I A318818 #4 Sep 04 2018 11:28:45
%S A318818 0,1,1,3,9,23,60,166,447,1219,3344,9214,25493,70853,197150,550259,
%T A318818 1539767,4314746,12112304,34063256,95904943,270375031,763193304,
%U A318818 2156328194,6098563949,17264760959,48912296290,138683094562,393514686620,1117304554815,3174397805762
%N A318818 Number of rooted trees with n nodes such that three equals the maximal number of subtrees of the same size extending from the same node.
%H A318818 Alois P. Heinz, <a href="/A318818/b318818.txt">Table of n, a(n) for n = 3..2158</a>
%p A318818 g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318818       binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p A318818     end:
%p A318818 a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(3):
%p A318818 seq(a(n), n=3..33);
%Y A318818 Column k=3 of A318754.
%K A318818 nonn
%O A318818 3,4
%A A318818 _Alois P. Heinz_, Sep 04 2018