A329053 Number of bicolored acyclic graphs on n unlabeled nodes.

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

Offset: 0

Author

Andrew Howroyd, Nov 02 2019

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Antidiagonal sums of A329052.

Cf. A122086.

Programs

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)))}

Formula

Euler transform of A122086.