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A220816 Number of rooted binary MUL-trees with n leaves on the label set [3]. 2

%I

%S 3,6,18,75,333,1620,8208,43188,232947,1282824,7178598,40711158,

%T 233445483,1351255608,7884677052,46330220604,273905815095,

%U 1628113352418,9724235975136,58330497033576,351252593186211,2122598374680816,12867757823745036,78235685862460893

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

%H Andrew Howroyd, <a href="/A220816/b220816.txt">Table of n, a(n) for n = 1..200</a>

%H V. P. Johnson, <a href="http://people.math.sc.edu/czabarka/Theses/JohnsonThesis.pdf">Enumeration Results on Leaf Labeled Trees</a>, Ph. D. Dissertation, Univ. Southern Calif., 2012.

%p a:= proc(n) option remember; `if`(n<2, 3*n, `if`(n::odd, 0,

%p (t-> t*(1-t)/2)(a(n/2)))+add(a(i)*a(n-i), i=1..n/2))

%p end:

%p seq(a(n), n=1..25); # _Alois P. Heinz_, Sep 23 2018

%t 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}]];

%t Array[a, 25] (* _Jean-Fran├žois Alcover_, Sep 02 2019, after _Alois P. Heinz_ *)

%Y Column 3 of A319539.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 22 2012

%E a(7) corrected and terms a(11) and beyond from _Andrew Howroyd_, Sep 22 2018

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Last modified September 18 10:11 EDT 2020. Contains 337166 sequences. (Running on oeis4.)