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%I #6 Sep 11 2017 17:09:52
%S 0,1,1,2,5,11,30,80,228,656,1945,5835,17808,54881,170951,536726,
%T 1697774,5403629,17295686,55630538,179726346,582942079,1897565974,
%U 6196973039,20297954197,66666192488,219505550167,724415274090,2395838962114,7939424272536
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than four.
%H Alois P. Heinz, <a href="/A292210/b292210.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, 4)))
%p end:
%p seq(a(n), n=0..35);
%Y Column k=4 of A292085.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Sep 11 2017
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