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Number of rooted trees with n nodes such that ten equals the maximal number of isomorphic subtrees extending from the same node.
2

%I #6 Sep 04 2018 18:51:44

%S 0,1,1,3,8,22,60,167,465,1306,3681,10423,29598,84313,240753,689013,

%T 1975659,5674795,16324964,47028023,135644560,391688786,1132214211,

%U 3275875432,9486452173,27493411246,79739872605,231430858159,672117007940,1953114145155,5678747077372

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

%H Alois P. Heinz, <a href="/A318867/b318867.txt">Table of n, a(n) for n = 10..2139</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))(10):

%p seq(a(n), n=10..40);

%Y Column k=10 of A318758.

%K nonn

%O 10,4

%A _Alois P. Heinz_, Sep 04 2018