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%I #5 Sep 11 2017 19:28:29
%S 0,1,1,2,5,12,33,90,261,766,2311,7065,21955,68921,218640,699161,
%T 2252410,7301482,23802026,77973162,256565366,847555502,2809934472,
%U 9346232579,31179372180,104298865434,349766936468,1175657140783,3960143985167,13366048810561
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than nine.
%H Alois P. Heinz, <a href="/A292215/b292215.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p b:= proc(n, i, v) 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)+j-1, j)*
%p b(n-i*j, i-1, v-j), j=0..min(n/i, v)))))
%p end:
%p a:= proc(n) option remember; `if`(n<2, n,
%p add(b(n, n+1-j, j), j=2..min(n, 9)))
%p end:
%p seq(a(n), n=0..35);
%Y Column k=9 of A292085.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Sep 11 2017
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