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A318866 Number of rooted trees with n nodes such that nine equals the maximal number of isomorphic subtrees extending from the same node.

%I A318866 #6 Sep 05 2018 08:22:52
%S A318866 0,1,1,3,8,22,60,167,465,1306,3682,10423,29597,84309,240735,688941,
%T A318866 1975403,5673911,16322021,47018394,135613559,391590017,1131902426,
%U A318866 3274897873,9483405008,27483957321,79710659583,231340894684,671840776074,1952268143504,5676161896298
%N A318866 Number of rooted trees with n nodes such that nine equals the maximal number of isomorphic subtrees extending from the same node.
%H A318866 Alois P. Heinz, <a href="/A318866/b318866.txt">Table of n, a(n) for n = 9..2138</a>
%p A318866 h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
%p A318866       `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
%p A318866     end:
%p A318866 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318866       add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
%p A318866     end:
%p A318866 A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
%p A318866 a:= n-> (k-> A(n, k)-A(n, k-1))(9):
%p A318866 seq(a(n), n=9..39);
%Y A318866 Column k=9 of A318758.
%K A318866 nonn
%O A318866 9,4
%A A318866 _Alois P. Heinz_, Sep 04 2018