A244708 - OEIS

%I #5 Jul 08 2014 09:14:15

%S 1,1,3,6,15,31,74,159,363,799,1800,3988,8945,19893,44486,99153,221520,

%T 494187,1103789,2463834,5502927,12288076,27448039,61308387,136966368,

%U 305999360,683733350,1527844853,3414432569,7631131801,17056871547,38127833992,85235556468

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

%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="/A244708/b244708.txt">Table of n, a(n) for n = 8..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, 7$2):

%p seq(a(n), n=8..50);

%Y Column k=7 of A244657.

%K nonn

%O 8,3

%A _Alois P. Heinz_, Jul 04 2014