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A318856 Number of rooted trees with n nodes such that no more than nine isomorphic subtrees extend from the same node.

%I A318856 #5 Sep 04 2018 18:03:07
%S A318856 0,1,1,2,4,9,20,48,115,286,719,1841,4764,12481,32960,87776,235286,
%T A318856 634585,1720432,4686643,12820514,35205695,97009447,268152808,
%U A318856 743354184,2066114828,5756601016,16075023964,44982030666,126114489722,354219135234,996572101259
%N A318856 Number of rooted trees with n nodes such that no more than nine isomorphic subtrees extend from the same node.
%H A318856 Alois P. Heinz, <a href="/A318856/b318856.txt">Table of n, a(n) for n = 0..2136</a>
%p A318856 h:= proc(n, m, t) option remember; `if`(m=0, binomial(n+t, t),
%p A318856       `if`(n=0, 0, add(h(n-1, m-j, t+1), j=1..min(9, m))))
%p A318856     end:
%p A318856 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318856       add(b(n-i*j, i-1)*h(a(i), j, 0), j=0..n/i)))
%p A318856     end:
%p A318856 a:= n-> `if`(n<2, n, b(n-1$2)):
%p A318856 seq(a(n), n=0..35);
%Y A318856 Column k=9 of A318757.
%K A318856 nonn
%O A318856 0,4
%A A318856 _Alois P. Heinz_, Sep 04 2018