A066351 Bisection of A007059.

1, 2, 5, 14, 43, 140, 472, 1628, 5719, 20388, 73562, 268066, 984911, 3643570, 13557020, 50691978, 190353370, 717457656, 2713061899, 10289600164, 39127877886, 149147692734, 569767908076, 2180978471298, 8363866011929, 32129445138352, 123618810558184

Offset: 0

Author

N. J. A. Sloane, Dec 19 2001

Keywords

• nonn
• easy

References

• R. Kemp, Balanced ordered trees, Random Structures and Algorithms, 5, 1994, 99-121.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      `if`(m=0, add(b(n-j, j), j=1..n),
      add(b(n-j, min(n-j, m)), j=1..min(n, m))))
    end:
a:= n-> b(2*n, 0):
seq(a(n), n=0..40);  # Alois P. Heinz, May 13 2014

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, 1, If[m == 0, Sum[b[n - j, j], {j, 1, n} ], Sum[b[n - j, Min[n - j, m]], {j, 1, Min[n, m]}]]]; a[n_] := b[2*n, 0]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Dec 22 2016, after Alois P. Heinz *)

Formula

Conjecture: a(n) ~ 0.721... * 4^n / n. - Vaclav Kotesovec, Aug 25 2014

Extensions

More terms from Emeric Deutsch, Jun 10 2004