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

%I A220816 #18 Sep 02 2019 15:21:53
%S A220816 3,6,18,75,333,1620,8208,43188,232947,1282824,7178598,40711158,
%T A220816 233445483,1351255608,7884677052,46330220604,273905815095,
%U A220816 1628113352418,9724235975136,58330497033576,351252593186211,2122598374680816,12867757823745036,78235685862460893
%N A220816 Number of rooted binary MUL-trees with n leaves on the label set [3].
%H A220816 Andrew Howroyd, <a href="/A220816/b220816.txt">Table of n, a(n) for n = 1..200</a>
%H A220816 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 A220816 a:= proc(n) option remember; `if`(n<2, 3*n, `if`(n::odd, 0,
%p A220816       (t-> t*(1-t)/2)(a(n/2)))+add(a(i)*a(n-i), i=1..n/2))
%p A220816     end:
%p A220816 seq(a(n), n=1..25);  # _Alois P. Heinz_, Sep 23 2018
%t A220816 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 A220816 Array[a, 25] (* _Jean-François Alcover_, Sep 02 2019, after _Alois P. Heinz_ *)
%Y A220816 Column 3 of A319539.
%K A220816 nonn
%O A220816 1,1
%A A220816 _N. J. A. Sloane_, Dec 22 2012
%E A220816 a(7) corrected and terms a(11) and beyond from _Andrew Howroyd_, Sep 22 2018