A102580 Number of n-node labeled connected digraphs whose underlying graphs are mating graphs, cf. A006024.

1, 1, 3, 27, 2025, 566190, 625831920, 2774192113350, 49208948146347570, 3472093007861482740960, 971461407155771477392032600, 1076446082528185671934674675023160, 4723701978908086606944984284949329285400, 82155133922723780601138029235949809990647219040

Offset: 0

Author

Goran Kilibarda, Zoran Maksimovic, Vladeta Jovovic, Jan 21 2005

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A006024, A102579 (not necessarily connected), A102597 (oriented), A102598 (unlabeled), A369283.

Programs

PARI

\\ b(n) is A102579(n); permcount, edges defined in A369283.
b(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 3^w)); s}
seq(n) = {Vec(serlaplace(1 + x + log(sum(k=0, n, b(k)*x^k/k!, O(x*x^n))/(1 + x))))} \\ Andrew Howroyd, Jan 20 2024

Formula

E.g.f.: 1 + x + log(B(x)/(1 + x)) where B(x) is the e.g.f. of A102579. - Andrew Howroyd, Jan 20 2024

Extensions

a(0)=1 prepended and a(12) onwards from Andrew Howroyd, Jan 20 2024