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