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A220816 Number of rooted binary MUL-trees with n leaves on the label set [3]. 2
3, 6, 18, 75, 333, 1620, 8208, 43188, 232947, 1282824, 7178598, 40711158, 233445483, 1351255608, 7884677052, 46330220604, 273905815095, 1628113352418, 9724235975136, 58330497033576, 351252593186211, 2122598374680816, 12867757823745036, 78235685862460893 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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-Fran├žois Alcover, Sep 02 2019, after Alois P. Heinz *)

CROSSREFS

Column 3 of A319539.

Sequence in context: A178789 A102962 A076510 * A038060 A135504 A307334

Adjacent sequences:  A220813 A220814 A220815 * A220817 A220818 A220819

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 22 2012

EXTENSIONS

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

STATUS

approved

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)