A244707 - OEIS

%I #5 Jul 08 2014 09:11:07

%S 1,1,3,6,15,31,74,157,359,786,1766,3895,8710,19287,42987,95437,212468,

%T 472204,1050940,2337221,5201558,11573156,25759514,57332239,127633669,

%U 284148877,632704464,1408925270,3137861761,6989057709,15568767849,34684141315,77277619879

%N Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 6.

%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="/A244707/b244707.txt">Table of n, a(n) for n = 7..900</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, 6$2):

%p seq(a(n), n=7..50);

%Y Column k=6 of A244657.

%K nonn

%O 7,3

%A _Alois P. Heinz_, Jul 04 2014