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%I #4 Sep 04 2018 12:01:22
%S 0,1,1,3,8,22,61,168,465,1302,3659,10333,29255,83096,236609,675311,
%T 1931235,5532421,15873557,45608348,131208906,377906025,1089573851,
%U 3144456980,9082730826,26256633715,75960348880,219905556560,637038643771,1846531053341,5355395451034
%N Number of rooted trees with n nodes such that five equals the maximal number of subtrees of the same size extending from the same node.
%H Alois P. Heinz, <a href="/A318820/b318820.txt">Table of n, a(n) for n = 5..2138</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))(5):
%p seq(a(n), n=5..35);
%Y Column k=5 of A318754.
%K nonn
%O 5,4
%A _Alois P. Heinz_, Sep 04 2018
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