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A318867 Number of rooted trees with n nodes such that ten equals the maximal number of isomorphic subtrees extending from the same node.

%I A318867 #6 Sep 04 2018 18:51:44
%S A318867 0,1,1,3,8,22,60,167,465,1306,3681,10423,29598,84313,240753,689013,
%T A318867 1975659,5674795,16324964,47028023,135644560,391688786,1132214211,
%U A318867 3275875432,9486452173,27493411246,79739872605,231430858159,672117007940,1953114145155,5678747077372
%N A318867 Number of rooted trees with n nodes such that ten equals the maximal number of isomorphic subtrees extending from the same node.
%H A318867 Alois P. Heinz, <a href="/A318867/b318867.txt">Table of n, a(n) for n = 10..2139</a>
%p A318867 h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
%p A318867       `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
%p A318867     end:
%p A318867 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318867       add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
%p A318867     end:
%p A318867 A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
%p A318867 a:= n-> (k-> A(n, k)-A(n, k-1))(10):
%p A318867 seq(a(n), n=10..40);
%Y A318867 Column k=10 of A318758.
%K A318867 nonn
%O A318867 10,4
%A A318867 _Alois P. Heinz_, Sep 04 2018