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A329053
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Number of bicolored acyclic graphs on n unlabeled nodes.
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3
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1, 2, 4, 8, 16, 32, 65, 134, 280, 598, 1300, 2884, 6516, 15008, 35147, 83680, 202139, 494982, 1226753, 3074146, 7779561, 19863702, 51125018, 132541616, 345867101, 907922596, 2396276355, 6355845398, 16934718359, 45309972502, 121697068925, 328029259192
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OFFSET
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0,2
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COMMENTS
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The two color classes are not interchangeable. Adjacent nodes cannot have the same color.
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LINKS
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FORMULA
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PROG
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(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
seq(n)={concat([1], EulerT(Vec(2*TreeGf(n) - TreeGf(n)^2)))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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