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A244711 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 10.

%I A244711 #4 Jul 08 2014 09:21:24
%S A244711 1,1,3,6,15,31,74,159,365,805,1819,4039,9085,20255,45421,101498,
%T A244711 227374,508571,1138954,2548992,5708220,12779899,28621759,64097135,
%U A244711 143571116,321590093,720437987,1614033142,3616368570,8103267171,18158695095,40694685268,91205979165
%N A244711 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 10.
%C A244711 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 A244711 Alois P. Heinz, <a href="/A244711/b244711.txt">Table of n, a(n) for n = 11..400</a>
%p A244711 b:= proc(n, i, h, v) option remember; `if`(n=0,
%p A244711       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A244711       `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
%p A244711        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
%p A244711     end:
%p A244711 A:= proc(n, k) option remember;
%p A244711       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k,n-1)))
%p A244711     end:
%p A244711 a:= n-> b(n-1$2, 10$2):
%p A244711 seq(a(n), n=11..50);
%Y A244711 Column k=10 of A244657.
%K A244711 nonn
%O A244711 11,3
%A A244711 _Alois P. Heinz_, Jul 04 2014