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A318855 Number of rooted trees with n nodes such that no more than eight isomorphic subtrees extend from the same node.

%I A318855 #5 Sep 04 2018 17:54:37
%S A318855 0,1,1,2,4,9,20,48,115,286,718,1840,4761,12473,32938,87716,235119,
%T A318855 634120,1719126,4682961,12810091,35176098,96925138,267912073,
%U A318855 742665243,2064139425,5750927105,16058701943,44935012272,125978876163,353827545217,995440198833
%N A318855 Number of rooted trees with n nodes such that no more than eight isomorphic subtrees extend from the same node.
%H A318855 Alois P. Heinz, <a href="/A318855/b318855.txt">Table of n, a(n) for n = 0..2136</a>
%p A318855 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318855       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(8, m))))
%p A318855     end:
%p A318855 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318855       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318855     end:
%p A318855 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318855 seq(a(n), n=0..35);
%Y A318855 Column k=8 of A318757.
%K A318855 nonn
%O A318855 0,4
%A A318855 _Alois P. Heinz_, Sep 04 2018