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%I #6 Sep 12 2017 11:55:51
%S 1,2,7,23,78,262,893,3040,10410,35718,122918,423861,1464642,5069475,
%T 17574187,61007028,212044176,737835578,2570028204,8960286527,
%U 31266462620,109188954531,381589000393,1334464142298,4669723965497,16350466246944,57280522330579
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals nine.
%H Alois P. Heinz, <a href="/A292235/b292235.txt">Table of n, a(n) for n = 9..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p b:= proc(n, i, v, k) option remember; `if`(n=0,
%p `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p `if`(v=n, 1, add(binomial(A(i, k)+j-1, j)*
%p b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
%p end:
%p A:= proc(n, k) option remember; `if`(n<2, n,
%p add(b(n, n+1-j, j, k), j=2..min(n, k)))
%p end:
%p a:= n-> A(n, 9)-A(n, 8):
%p seq(a(n), n=9..40);
%Y Column k=9 of A292086.
%K nonn
%O 9,2
%A _Alois P. Heinz_, Sep 12 2017
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