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%I #4 Sep 04 2018 11:42:01
%S 0,1,1,3,8,23,61,167,461,1288,3593,10084,28381,80218,227156,644864,
%T 1834290,5227297,14919502,42644478,122047963,349716506,1003120145,
%U 2880163515,8276937322,23805829084,68521035251,197365718477,568859465838,1640609651599,4734261078026
%N Number of rooted trees with n nodes such that four equals the maximal number of subtrees of the same size extending from the same node.
%H Alois P. Heinz, <a href="/A318819/b318819.txt">Table of n, a(n) for n = 4..2143</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))(4):
%p seq(a(n), n=4..34);
%Y Column k=4 of A318754.
%K nonn
%O 4,4
%A _Alois P. Heinz_, Sep 04 2018
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