A102598 -id:A102598 - cp's OEIS frontend

A102579 Number of n-node labeled digraphs whose underlying graphs are mating graphs, cf. A006024.

1, 1, 3, 36, 2160, 577260, 629332740, 2778611237640, 49231195558057800, 3472536190055702938560, 971496134741368475512176960, 1076456769176854177692230640971520, 4723714896453453856832035698858163891200, 82155195331101404797144020808246647196388279040

Offset: 0

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

nonn

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

Cf. A006024, A102580 (connected), A102596 (oriented), A102598, A369283.

\\ permcount, edges defined in A369283.
a(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + 3^w)); s} \\ Andrew Howroyd, Jan 20 2024

a(n) = Sum_{k>=0} 3^k * A369283(n,k). - Andrew Howroyd, Jan 20 2024

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

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

Original entry on oeis.org

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

Offset: 0

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

nonn

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

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

\\ 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

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

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

cp's OEIS Frontend

A102579 Number of n-node labeled digraphs whose underlying graphs are mating graphs, cf. A006024.

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