%I #5 Jul 08 2014 09:16:25

%S 1,1,3,6,15,31,74,159,365,803,1813,4022,9038,20128,45093,100656,

%T 225263,503320,1126045,2517487,5631913,12596046,28181168,63045684,

%U 141071758,315668674,706452161,1581088178,3538954508,7921759060,17733983146,39702719910,88893039358

%N Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 8.

%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="/A244709/b244709.txt">Table of n, a(n) for n = 9..500</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, 8$2):

%p seq(a(n), n=9..50);

%Y Column k=8 of A244657.

%K nonn

%O 9,3

%A _Alois P. Heinz_, Jul 04 2014