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A318861 Number of rooted trees with n nodes such that four equals the maximal number of isomorphic subtrees extending from the same node.

%I A318861 #5 Sep 05 2018 10:09:15
%S A318861 0,1,1,3,8,23,61,167,461,1285,3587,10069,28350,80101,226861,644064,
%T A318861 1832113,5221138,14902620,42597586,121917123,349343846,1002080752,
%U A318861 2877234480,8268665140,23782254063,68454314588,197176382059,568320901793,1639070974728,4729877188814
%N A318861 Number of rooted trees with n nodes such that four equals the maximal number of isomorphic subtrees extending from the same node.
%H A318861 Alois P. Heinz, <a href="/A318861/b318861.txt">Table of n, a(n) for n = 4..2143</a>
%p A318861 h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
%p A318861       `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
%p A318861     end:
%p A318861 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A318861       add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
%p A318861     end:
%p A318861 A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
%p A318861 a:= n-> (k-> A(n, k)-A(n, k-1))(4):
%p A318861 seq(a(n), n=4..34);
%Y A318861 Column k=4 of A318758.
%K A318861 nonn
%O A318861 4,4
%A A318861 _Alois P. Heinz_, Sep 04 2018