A244712 Number of 2n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) n.

0, 1, 1, 3, 6, 15, 31, 74, 159, 365, 805, 1819, 4041, 9091, 20274, 45474, 101644, 227755, 509559, 1141446, 2555232, 5723626, 12817678, 28713594, 64319189, 144104857, 322867573, 723482538, 1621264326, 3633487621, 8143682973, 18253865341, 40918282628, 91730206467

Offset: 0

Author

Alois P. Heinz, Jul 04 2014

Keywords

• nonn

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

• Vaclav Kotesovec, Table of n, a(n) for n = 0..193 (terms 0..70 from Alois P. Heinz)

Crossrefs

Cf. A244657.

Programs

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 b(2*n-1$2, n$2):
seq(a(n), n=0..40);

Mathematica

b[n_, i_, h_, v_] := b[n, i, h, v] = If[n == 0, If[v == 0, 1, 0], If[i<1 || v<1 || nJean-François Alcover, Feb 26 2017, after Alois P. Heinz *)

Formula

a(n) = A244657(2n,n).