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%I #6 Sep 12 2017 11:54:26
%S 1,2,7,23,77,256,861,2897,9800,33232,113012,385165,1315434,4500398,
%T 15421463,52919299,181826880,625467087,2153816295,7423887771,
%U 25611710370,88430103927,305555059139,1056532822348,3655607694207,12656112780583,43841784746311
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals five.
%H Alois P. Heinz, <a href="/A292231/b292231.txt">Table of n, a(n) for n = 5..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, 5)-A(n, 4):
%p seq(a(n), n=5..35);
%Y Column k=5 of A292086.
%K nonn
%O 5,2
%A _Alois P. Heinz_, Sep 12 2017
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