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%I #5 Sep 11 2017 17:53:28
%S 0,1,1,2,5,12,32,87,251,733,2201,6696,20705,64681,204183,649738,
%T 2082939,6719063,21796084,71052001,232645645,764768959,2523033061,
%U 8350789334,27721841968,92277902858,307935654094,1029970333229,3452371784462,11595031966743
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than five.
%H Alois P. Heinz, <a href="/A292211/b292211.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, 5)))
%p end:
%p seq(a(n), n=0..35);
%Y Column k=5 of A292085.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Sep 11 2017
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