A244706 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 5.

1, 1, 3, 6, 15, 31, 72, 153, 346, 752, 1673, 3661, 8108, 17814, 39349, 86646, 191251, 421596, 930519, 2052789, 4531648, 10002857, 22088709, 48780279, 107757048, 238069894, 526096509, 1162775782, 2570487392, 5683401236, 12568472173, 27799055016, 61496981626

Offset

6,3

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 = 6..1000

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, 5$2):
seq(a(n), n=6..50);

Crossrefs

Column k=5 of A244657.

Sequence in context: A256281 A034739 A276670 * A097941 A317792 A293732

Adjacent sequences: A244703 A244704 A244705 * A244707 A244708 A244709

Keyword

nonn

Author

Alois P. Heinz, Jul 04 2014

Status

approved