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A244708 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 7.

%I A244708 #5 Jul 08 2014 09:14:15
%S A244708 1,1,3,6,15,31,74,159,363,799,1800,3988,8945,19893,44486,99153,221520,
%T A244708 494187,1103789,2463834,5502927,12288076,27448039,61308387,136966368,
%U A244708 305999360,683733350,1527844853,3414432569,7631131801,17056871547,38127833992,85235556468
%N A244708 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 7.
%C A244708 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 A244708 Alois P. Heinz, <a href="/A244708/b244708.txt">Table of n, a(n) for n = 8..500</a>
%p A244708 b:= proc(n, i, h, v) option remember; `if`(n=0,
%p A244708       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A244708       `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
%p A244708        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
%p A244708     end:
%p A244708 A:= proc(n, k) option remember;
%p A244708       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k,n-1)))
%p A244708     end:
%p A244708 a:= n-> b(n-1$2, 7$2):
%p A244708 seq(a(n), n=8..50);
%Y A244708 Column k=7 of A244657.
%K A244708 nonn
%O A244708 8,3
%A A244708 _Alois P. Heinz_, Jul 04 2014