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

1, 1, 3, 6, 15, 31, 74, 159, 365, 805, 1819, 4039, 9085, 20255, 45421, 101498, 227374, 508571, 1138954, 2548992, 5708220, 12779899, 28621759, 64097135, 143571116, 321590093, 720437987, 1614033142, 3616368570, 8103267171, 18158695095, 40694685268, 91205979165

Offset

11,3

Comments

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 11..400

Maple

b:= proc(n, i, h, v) option remember; `if`(n=0,
      `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
      `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, j)
       *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v)))))
    end:
A:= proc(n, k) option remember;
      `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
    end:
a:= n-> b(n-1$2, 10$2):
seq(a(n), n=11..50);

Crossrefs

Column k=10 of A244657.

Sequence in context: A244708 A244709 A244710 * A244712 A006961 A316219

Adjacent sequences: A244708 A244709 A244710 * A244712 A244713 A244714

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved