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

0,3

Links

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

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

Prog

(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

Crossrefs

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

Sequence in context: A305843 A192341 A191511 * A051576 A184278 A158113

Adjacent sequences: A102577 A102578 A102579 * A102581 A102582 A102583

Keyword

nonn

Author

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

Extensions

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

Status

approved