A026865 Number of labeled chain graphs.

1, 4, 50, 1688, 142624, 28903216, 13663125680, 14762428500992, 35888247726445696, 193881737041021767424, 2304330431696396880081920, 59754569042355286885937374208, 3357295191788547946256710562827264

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Bertran Steinsky, Enumeration of labelled chain graphs and labeled essential directed acyclic graphs, Discrete Mathematics, 270 (2003), 267-278.

Formula

a(n) = -Sum_{k=1..n} binomial(n, k) * b(k) * a(n - k) * 2^(k*(n-k)) with a(0) = b(0) = 1 and b(n) = -Sum_{k=0..n-1} binomial(n, k) * b(k) * 2^(binomial(n-r, 2)) [from Steinsky]. - Sean A. Irvine, Oct 15 2019

Crossrefs

Sequence in context: A234714 A201829 A201209 * A016078 A327229 A231832

Adjacent sequences: A026862 A026863 A026864 * A026866 A026867 A026868

Keyword

nonn

Author

Detlef Pauly (dettodet(AT)yahoo.de), Aug 22 2003

Status

approved