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A244710 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 9.

%I A244710 #5 Jul 08 2014 09:19:35
%S A244710 1,1,3,6,15,31,74,159,365,805,1817,4035,9072,20221,45328,101263,
%T A244710 226767,507067,1135206,2539827,5685851,12725874,28491634,63785789,
%U A244710 142828392,319826118,716260116,1604170013,3593139239,8048694851,18030750419,40395321587,90506748160
%N A244710 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 9.
%C A244710 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 A244710 Alois P. Heinz, <a href="/A244710/b244710.txt">Table of n, a(n) for n = 10..500</a>
%p A244710 b:= proc(n, i, h, v) option remember; `if`(n=0,
%p A244710       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
%p A244710       `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
%p A244710        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
%p A244710     end:
%p A244710 A:= proc(n, k) option remember;
%p A244710       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k,n-1)))
%p A244710     end:
%p A244710 a:= n-> b(n-1$2, 9$2):
%p A244710 seq(a(n), n=10..50);
%Y A244710 Column k=9 of A244657.
%K A244710 nonn
%O A244710 10,3
%A A244710 _Alois P. Heinz_, Jul 04 2014