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

0,2

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

Formula

Euler transform of A122086.

Prog

(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)))}

Crossrefs

Antidiagonal sums of A329052.

Cf. A122086.

Sequence in context: A367652 A023421 A098051 * A084637 A100137 A325917

Adjacent sequences: A329050 A329051 A329052 * A329054 A329055 A329056

Keyword

nonn

Author

Andrew Howroyd, Nov 02 2019

Status

approved