cp's OEIS Frontend

A318824 Number of rooted trees with n nodes such that nine equals the maximal number of subtrees of the same size extending from the same node.

%I A318824 #4 Sep 04 2018 15:34:00
%S A318824 0,1,1,3,8,22,60,167,465,1306,3682,10423,29597,84309,240735,688941,
%T A318824 1975403,5673911,16322021,47018402,135613575,391590057,1131902512,
%U A318824 3274898117,9483405678,27483959193,79710664789,231340909288,671840817408,1952268260256,5676162227486
%N A318824 Number of rooted trees with n nodes such that nine equals the maximal number of subtrees of the same size extending from the same node.
%H A318824 Alois P. Heinz, <a href="/A318824/b318824.txt">Table of n, a(n) for n = 9..2138</a>
%p A318824 g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318824       binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p A318824     end:
%p A318824 a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(9):
%p A318824 seq(a(n), n=9..39);
%Y A318824 Column k=9 of A318754.
%K A318824 nonn
%O A318824 9,4
%A A318824 _Alois P. Heinz_, Sep 04 2018