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Number of bicolored acyclic graphs on n unlabeled nodes.
3

%I #9 Nov 05 2019 05:52:29

%S 1,2,4,8,16,32,65,134,280,598,1300,2884,6516,15008,35147,83680,202139,

%T 494982,1226753,3074146,7779561,19863702,51125018,132541616,345867101,

%U 907922596,2396276355,6355845398,16934718359,45309972502,121697068925,328029259192

%N Number of bicolored acyclic graphs on n unlabeled nodes.

%C The two color classes are not interchangeable. Adjacent nodes cannot have the same color.

%H Andrew Howroyd, <a href="/A329053/b329053.txt">Table of n, a(n) for n = 0..500</a>

%F Euler transform of A122086.

%o (PARI)

%o EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}

%o 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)}

%o seq(n)={concat([1], EulerT(Vec(2*TreeGf(n) - TreeGf(n)^2)))}

%Y Antidiagonal sums of A329052.

%Y Cf. A122086.

%K nonn

%O 0,2

%A _Andrew Howroyd_, Nov 02 2019