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

%I #4 Sep 04 2018 15:49:36

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

%T 1975659,5674795,16324964,47028023,135644560,391688795,1132214229,

%U 3275875477,9486452270,27493411521,79739873360,231430860268,672117013805,1953114161607,5678747123701

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

%H Alois P. Heinz, <a href="/A318825/b318825.txt">Table of n, a(n) for n = 10..2139</a>

%p g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

%p binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))

%p end:

%p a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(10):

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

%Y Column k=10 of A318754.

%K nonn

%O 10,4

%A _Alois P. Heinz_, Sep 04 2018