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A318864 Number of rooted trees with n nodes such that seven equals the maximal number of isomorphic subtrees extending from the same node.

%I A318864 #5 Sep 05 2018 09:05:18
%S A318864 0,1,1,3,8,22,60,167,466,1307,3681,10418,29575,84219,240407,687802,
%T A318864 1971576,5661335,16281377,46888590,135202932,390300559,1127877757,
%U A318864 3262398334,9444747407,27364824226,79344643855,230219356666,668412171376,1941808202980,5644309042885
%N A318864 Number of rooted trees with n nodes such that seven equals the maximal number of isomorphic subtrees extending from the same node.
%H A318864 Alois P. Heinz, <a href="/A318864/b318864.txt">Table of n, a(n) for n = 7..2137</a>
%p A318864 h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
%p A318864       `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
%p A318864     end:
%p A318864 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318864       add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
%p A318864     end:
%p A318864 A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
%p A318864 a:= n-> (k-> A(n, k)-A(n, k-1))(7):
%p A318864 seq(a(n), n=7..37);
%Y A318864 Column k=7 of A318758.
%K A318864 nonn
%O A318864 7,4
%A A318864 _Alois P. Heinz_, Sep 04 2018