%I #5 Jul 08 2014 09:02:59

%S 1,1,3,6,15,31,72,153,346,752,1673,3661,8108,17814,39349,86646,191251,

%T 421596,930519,2052789,4531648,10002857,22088709,48780279,107757048,

%U 238069894,526096509,1162775782,2570487392,5683401236,12568472173,27799055016,61496981626

%N Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 5.

%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="/A244706/b244706.txt">Table of n, a(n) for n = 6..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, 5$2):

%p seq(a(n), n=6..50);

%Y Column k=5 of A244657.

%K nonn

%O 6,3

%A _Alois P. Heinz_, Jul 04 2014