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Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than seven.
2

%I #5 Sep 11 2017 18:45:48

%S 0,1,1,2,5,12,33,90,260,763,2302,7035,21854,68581,217485,695229,

%T 2238965,7255380,23643501,77426852,254678757,841028918,2787320206,

%U 9267764857,30906754731,103350631437,346465277423,1164150100182,3920004155435,13225916804136

%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than seven.

%H Alois P. Heinz, <a href="/A292213/b292213.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, 7)))

%p end:

%p seq(a(n), n=0..35);

%Y Column k=7 of A292085.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Sep 11 2017