A220816 Number of rooted binary MUL-trees with n leaves on the label set [3].

3, 6, 18, 75, 333, 1620, 8208, 43188, 232947, 1282824, 7178598, 40711158, 233445483, 1351255608, 7884677052, 46330220604, 273905815095, 1628113352418, 9724235975136, 58330497033576, 351252593186211, 2122598374680816, 12867757823745036, 78235685862460893

Offset: 1

Author

N. J. A. Sloane, Dec 22 2012

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• V. P. Johnson, Enumeration Results on Leaf Labeled Trees, Ph. D. Dissertation, Univ. Southern Calif., 2012.

Crossrefs

Column 3 of A319539.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 3*n, `if`(n::odd, 0,
      (t-> t*(1-t)/2)(a(n/2)))+add(a(i)*a(n-i), i=1..n/2))
    end:
seq(a(n), n=1..25);  # Alois P. Heinz, Sep 23 2018

Mathematica

a[n_] := a[n] = If[n < 2, 3 n, If[OddQ[n], 0, (# (1 - #)/2 &)[a[n/2]]] + Sum[a[i] a[n - i], {i, 1, n/2}]];
Array[a, 25] (* Jean-François Alcover, Sep 02 2019, after Alois P. Heinz *)

Extensions

a(7) corrected and terms a(11) and beyond from Andrew Howroyd, Sep 22 2018