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A329053 Number of bicolored acyclic graphs on n unlabeled nodes. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A101333 A023421 A098051 * A084637 A100137 A325917

Adjacent sequences:  A329050 A329051 A329052 * A329054 A329055 A329056

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Nov 02 2019

STATUS

approved

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Last modified May 25 11:07 EDT 2020. Contains 334592 sequences. (Running on oeis4.)