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Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 4.
2

%I #5 Jul 08 2014 09:00:33

%S 1,1,3,6,15,29,68,140,312,660,1443,3084,6710,14425,31278,67508,146300,

%T 316424,685955,1486008,3223480,6992012,15179437,32960891,71617874,

%U 155661971,338508703,736401503,1602712182,3489454243,7600403101,16560519877,36097320801

%N Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 4.

%C In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.

%H Alois P. Heinz, <a href="/A244705/b244705.txt">Table of n, a(n) for n = 5..1000</a>

%p b:= proc(n, i, h, v) option remember; `if`(n=0,

%p `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,

%p `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)

%p *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))

%p end:

%p A:= proc(n, k) option remember;

%p `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k,n-1)))

%p end:

%p a:= n-> b(n-1$2, 4$2):

%p seq(a(n), n=5..50);

%Y Column k=4 of A244657.

%K nonn

%O 5,3

%A _Alois P. Heinz_, Jul 04 2014