cp's OEIS Frontend

A318817 Number of rooted trees with n nodes such that two equals the maximal number of subtrees of the same size extending from the same node.

%I A318817 #8 Sep 04 2018 11:14:12
%S A318817 0,1,1,4,9,22,54,139,346,892,2290,5945,15465,40527,106308,280629,
%T A318817 742107,1969394,5239322,13980900,37368692,100157418,268900827,
%U A318817 723400570,1949440608,5262932344,14227803491,38529294292,104473993774,283672750693,771229441388
%N A318817 Number of rooted trees with n nodes such that two equals the maximal number of subtrees of the same size extending from the same node.
%H A318817 Alois P. Heinz, <a href="/A318817/b318817.txt">Table of n, a(n) for n = 2..2213</a>
%p A318817 g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318817       binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p A318817     end:
%p A318817 a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(2):
%p A318817 seq(a(n), n=2..32);
%Y A318817 Column k=2 of A318754.
%K A318817 nonn
%O A318817 2,4
%A A318817 _Alois P. Heinz_, Sep 04 2018