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A119855
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Number of equicolorable rooted trees on 2n nodes.
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3
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1, 2, 9, 44, 249, 1506, 9687, 64803, 447666, 3169566, 22897260, 168168164, 1252391041, 9437809359, 71850420813, 551876468717, 4272100488830, 33299732401378, 261165251593743, 2059638535690473, 16324255856903830, 129969379170062142, 1039056925387672998
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OFFSET
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1,2
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COMMENTS
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For precise definition, recurrence and asymptotics see the Pippenger reference.
An equicolorable tree is a tree which can be colored with two colors with adjacent nodes having different colors and there being an equal number of nodes of each color. - Andrew Howroyd, May 21 2018
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REFERENCES
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N. Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math., 14 (2001), 93-115.
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LINKS
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PROG
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(PARI) \\ R is b.g.f of rooted trees x nodes, y in one part
R(n)={my(A=O(x)); for(j=1, 2*n, A = if(j%2, 1, y)*x*exp(sum(i=1, j, 1/i * subst(subst(A + x * O(x^(j\i)), x, x^i), y, y^i)))); A};
seq(n)={my(A=Pol(R(n))); my(r(x, y)=substvec(A, ['x, 'y], [x, y/x])); Vec(polcoeff(r(x, y/x), 0) + O(y*y^n))} \\ Andrew Howroyd, May 23 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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