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%I #5 Sep 05 2018 08:42:30
%S 0,1,1,3,8,22,60,167,465,1307,3682,10422,29593,84291,240663,688685,
%T 1974519,5670969,16312391,46987389,135514781,391278211,1130924824,
%U 3271850658,9473951229,27454745755,79620703854,231064697016,670994912068,1949683485967,5668279789793
%N Number of rooted trees with n nodes such that eight equals the maximal number of isomorphic subtrees extending from the same node.
%H Alois P. Heinz, <a href="/A318865/b318865.txt">Table of n, a(n) for n = 8..2137</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))(8):
%p seq(a(n), n=8..38);
%Y Column k=8 of A318758.
%K nonn
%O 8,4
%A _Alois P. Heinz_, Sep 04 2018
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