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A339782 Number of homeomorphically irreducible leaf colored trees with n leaves of 2 colors.

%I A339782 #10 Jan 10 2021 02:13:27
%S A339782 1,2,3,4,11,30,105,380,1555,6650,30091,140592,677396,3336280,16752485,
%T A339782 85444832,441757114,2310561412,12208670550,65088056150,349773085560,
%U A339782 1893030193232,10311145350621,56489805467868,311113902447810,1721697849252838,9569947189448379,53410284955104654
%N A339782 Number of homeomorphically irreducible leaf colored trees with n leaves of 2 colors.
%H A339782 Andrew Howroyd, <a href="/A339782/b339782.txt">Table of n, a(n) for n = 0..500</a>
%e A339782 There are two trees for a(4):
%e A339782           o         o    o
%e A339782           |         |    |
%e A339782       o---o---o     o----o
%e A339782           |         |    |
%e A339782           o         o    o
%e A339782 The first of these can have the 4 leaves colored in 5 indistinguishable ways and the second can have the 4 leaves colored in 6 indistinguishable ways so a(4) = 5 + 6 = 11.
%o A339782 (PARI) U(25, 2) \\ See A339779 for U(n,k).
%Y A339782 Column k=2 of A339779.
%K A339782 nonn
%O A339782 0,2
%A A339782 _Andrew Howroyd_, Dec 16 2020