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Number of unrooted binary leaf-multi-labeled trees with n leaves on the label set [2], with each label used at least once.
4

%I #17 Dec 15 2020 12:54:46

%S 0,1,2,4,10,27,74,226,710,2354,8010,28189,101094,370119,1375198,

%T 5181003,19740940,75990173,295100800,1155106357,4553312866,

%U 18063117153,72069297826,289053128879,1164870009786,4714970819402,19161572076550,78162885020942,319940035684684,1313799822309748

%N Number of unrooted binary leaf-multi-labeled trees with n leaves on the label set [2], with each label used at least once.

%H Andrew Howroyd, <a href="/A220829/b220829.txt">Table of n, a(n) for n = 1..500</a>

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

%F a(n) = A220826(n) - 2*A129860(n). - _Andrew Howroyd_, Dec 14 2020

%o (PARI) my(N=30); U(N,2) - 2*U(N,1) \\ See A339650 for U(n,k). - _Andrew Howroyd_, Dec 14 2020

%Y Column 2 of A339650.

%Y Cf. A129860, A220826.

%K nonn

%O 1,3

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

%E Terms a(11) and beyond from _Andrew Howroyd_, Dec 14 2020