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%I #8 Sep 04 2018 11:14:12
%S 0,1,1,4,9,22,54,139,346,892,2290,5945,15465,40527,106308,280629,
%T 742107,1969394,5239322,13980900,37368692,100157418,268900827,
%U 723400570,1949440608,5262932344,14227803491,38529294292,104473993774,283672750693,771229441388
%N Number of rooted trees with n nodes such that two equals the maximal number of subtrees of the same size extending from the same node.
%H Alois P. Heinz, <a href="/A318817/b318817.txt">Table of n, a(n) for n = 2..2213</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))(2):
%p seq(a(n), n=2..32);
%Y Column k=2 of A318754.
%K nonn
%O 2,4
%A _Alois P. Heinz_, Sep 04 2018
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