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A318863 Number of rooted trees with n nodes such that six equals the maximal number of isomorphic subtrees extending from the same node.

%I A318863 #5 Sep 05 2018 09:24:20
%S A318863 0,1,1,3,8,22,60,168,466,1306,3677,10400,29503,83964,239523,684855,
%T A318863 1961933,5630300,16182535,46576693,134225427,387254945,1118433179,
%U A318863 3233228736,9354963666,27089288339,78501221909,227643444368,660560681614,1917918979943,5571738217340
%N A318863 Number of rooted trees with n nodes such that six equals the maximal number of isomorphic subtrees extending from the same node.
%H A318863 Alois P. Heinz, <a href="/A318863/b318863.txt">Table of n, a(n) for n = 6..2137</a>
%p A318863 h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
%p A318863       `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
%p A318863     end:
%p A318863 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318863       add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
%p A318863     end:
%p A318863 A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
%p A318863 a:= n-> (k-> A(n, k)-A(n, k-1))(6):
%p A318863 seq(a(n), n=6..36);
%Y A318863 Column k=6 of A318758.
%K A318863 nonn
%O A318863 6,4
%A A318863 _Alois P. Heinz_, Sep 04 2018