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

1, 1, 3, 6, 15, 31, 74, 159, 365, 805, 1817, 4035, 9072, 20221, 45328, 101263, 226767, 507067, 1135206, 2539827, 5685851, 12725874, 28491634, 63785789, 142828392, 319826118, 716260116, 1604170013, 3593139239, 8048694851, 18030750419, 40395321587, 90506748160

Offset

10,3

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 = 10..500

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, 9$2):
seq(a(n), n=10..50);

Crossrefs

Column k=9 of A244657.

Sequence in context: A244707 A244708 A244709 * A244711 A244712 A006961

Adjacent sequences: A244707 A244708 A244709 * A244711 A244712 A244713

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved