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%I #4 Jul 08 2014 09:21:24
%S 1,1,3,6,15,31,74,159,365,805,1819,4039,9085,20255,45421,101498,
%T 227374,508571,1138954,2548992,5708220,12779899,28621759,64097135,
%U 143571116,321590093,720437987,1614033142,3616368570,8103267171,18158695095,40694685268,91205979165
%N Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 10.
%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="/A244711/b244711.txt">Table of n, a(n) for n = 11..400</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, 10$2):
%p seq(a(n), n=11..50);
%Y Column k=10 of A244657.
%K nonn
%O 11,3
%A _Alois P. Heinz_, Jul 04 2014
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