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A318850 Number of rooted trees with n nodes such that no more than three isomorphic subtrees extend from the same node.

%I A318850 #6 Sep 04 2018 16:56:12
%S A318850 0,1,1,2,4,8,18,43,102,250,623,1579,4042,10473,27356,72049,190991,
%T A318850 509384,1365586,3678369,9949452,27014550,73600711,201153143,551329088,
%U A318850 1515078957,4173575232,11522620375,31878127954,88362886345,245372235144,682508792835
%N A318850 Number of rooted trees with n nodes such that no more than three isomorphic subtrees extend from the same node.
%H A318850 Alois P. Heinz, <a href="/A318850/b318850.txt">Table of n, a(n) for n = 0..2158</a>
%p A318850 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318850       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(3, m))))
%p A318850     end:
%p A318850 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318850       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318850     end:
%p A318850 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318850 seq(a(n), n=0..35);
%Y A318850 Column k=3 of A318757.
%K A318850 nonn
%O A318850 0,4
%A A318850 _Alois P. Heinz_, Sep 04 2018