cp's OEIS Frontend

A318821 Number of rooted trees with n nodes such that six equals the maximal number of subtrees of the same size extending from the same node.

%I A318821 #4 Sep 04 2018 12:16:50
%S A318821 0,1,1,3,8,22,60,168,466,1306,3677,10400,29503,83969,239533,684880,
%T A318821 1961986,5630451,16182950,46577929,134228796,387264335,1118459507,
%U A318821 3233302665,9355173164,27089886520,78502923212,227648300409,660574571072,1917958785876,5571852459248
%N A318821 Number of rooted trees with n nodes such that six equals the maximal number of subtrees of the same size extending from the same node.
%H A318821 Alois P. Heinz, <a href="/A318821/b318821.txt">Table of n, a(n) for n = 6..2137</a>
%p A318821 g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A318821       binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p A318821     end:
%p A318821 a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(6):
%p A318821 seq(a(n), n=6..36);
%Y A318821 Column k=6 of A318754.
%K A318821 nonn
%O A318821 6,4
%A A318821 _Alois P. Heinz_, Sep 04 2018