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%I #8 Jan 20 2024 13:52:28
%S 1,1,3,36,2160,577260,629332740,2778611237640,49231195558057800,
%T 3472536190055702938560,971496134741368475512176960,
%U 1076456769176854177692230640971520,4723714896453453856832035698858163891200,82155195331101404797144020808246647196388279040
%N Number of n-node labeled digraphs whose underlying graphs are mating graphs, cf. A006024.
%H Andrew Howroyd, <a href="/A102579/b102579.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = Sum_{k>=0} 3^k * A369283(n,k). - _Andrew Howroyd_, Jan 20 2024
%o (PARI) \\ permcount, edges defined in A369283.
%o 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
%Y Cf. A006024, A102580 (connected), A102596 (oriented), A102598, A369283.
%K nonn
%O 0,3
%A Goran Kilibarda, Zoran Maksimovic, _Vladeta Jovovic_, Jan 21 2005
%E a(0)=1 prepended and a(12) onwards from _Andrew Howroyd_, Jan 20 2024
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