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%I #5 Sep 05 2018 10:27:09
%S 0,1,1,3,9,23,60,164,443,1209,3319,9150,25326,70335,195870,546823,
%T 1529935,4288662,12042447,33866604,95373852,268925258,759157224,
%U 2145298117,6068251826,17180172176,48680092670,138041661905,391725281701,1112360700816,3160707529077
%N Number of rooted trees with n nodes such that three equals the maximal number of isomorphic subtrees extending from the same node.
%H Alois P. Heinz, <a href="/A318860/b318860.txt">Table of n, a(n) for n = 3..2158</a>
%p h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
%p `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
%p end:
%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
%p end:
%p A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
%p a:= n-> (k-> A(n, k)-A(n, k-1))(3):
%p seq(a(n), n=3..33);
%Y Column k=3 of A318758.
%K nonn
%O 3,4
%A _Alois P. Heinz_, Sep 04 2018
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