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%I #11 Mar 13 2023 13:29:27
%S 1,3,16,99,717,5964,56701,611750,7432491,100838222,1514749135,
%T 24989362186,449429188211,8754181791029,183621843677724,
%U 4126714250580949,98932328702693666,2520187379996442269,67980528958530199837,1935753445850303203221,58025998739501873764826
%N Number of connected 3-regular multigraphs on 2n unlabeled nodes rooted at an oriented edge (or loop), loops allowed.
%C a(0) = 1 by convention. Loops add two to the degree of a node.
%F G.f.: B(x)/C(x) where B(x) is the g.f. of A352175 and C(x) is the g.f. of A129427.
%Y A352174 is the 4-regular version.
%Y Cf. A005967 (unrooted), A129427, A352175, A361412 (rooted at unoriented edge), A361447, A361448.
%K nonn
%O 0,2
%A _Andrew Howroyd_, Mar 12 2023