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%I #4 Sep 04 2018 14:46:19
%S 0,1,1,3,8,22,60,167,466,1307,3681,10418,29575,84219,240407,687808,
%T 1971588,5661365,16281441,46888772,135203432,390301957,1127881755,
%U 3262409450,9444778623,27364912377,79344893246,230220066260,668414195077,1941813994013,5644325624891
%N Number of rooted trees with n nodes such that seven equals the maximal number of subtrees of the same size extending from the same node.
%H Alois P. Heinz, <a href="/A318822/b318822.txt">Table of n, a(n) for n = 7..2137</a>
%p g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
%p end:
%p a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(7):
%p seq(a(n), n=7..37);
%Y Column k=7 of A318754.
%K nonn
%O 7,4
%A _Alois P. Heinz_, Sep 04 2018
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