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%I #7 Jan 01 2024 13:30:44
%S 1,1,91,1,176130
%N a(n) is the number of reduced instances in the stable marriage problem of order n that generate the maximum possible number of stable matchings.
%C Reduced instances (A351409) are fewer than all instances by a factor of n!(n-1)! due to participant-renaming isomorphism, analogous to reduced latin squares.
%C For n in [1,2,4], a(n) = 1 showing uniqueness up to isomorphism.
%H David F. Manlove, <a href="https://doi.org/10.1142/8591">Algorithmics of Matching Under Preferences</a>, World Scientific (2013) [Section 2.2.2].
%F a(n) = A344669(n) / A010790(n-1).
%F a(4) = A351430(10).
%F a(5) = A368419(0).
%Y Cf. A344669 (unreduced), A351430 (order 4), A368419 (order 5), A351409 (total reduced instances), A010790 (reduction factor offset by 1).
%K nonn,more,hard
%O 1,3
%A _Dan Eilers_, Dec 24 2023