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A137737 Number of circular permutations of the multiset {1,1,2,2,...,n,n} (up to rotations) with even distances between equal elements.

%I A137737 #5 Jun 29 2025 22:19:12
%S A137737 0,1,0,30,0,13560,0,27785520,0,162030637440,0,2156625389318400,0,
%T A137737 56857271240920550400,0,2686506065987036477184000,0,
%U A137737 211180868835057744408834048000,0,26072812428113877344085395644416000,0
%N A137737 Number of circular permutations of the multiset {1,1,2,2,...,n,n} (up to rotations) with even distances between equal elements.
%F A137737 For odd n, a(n) = 0. For even n, a(n) = (n!^3 / (n/2)!^2 / 2^n + n!) / (2n).
%F A137737 a(2n) = A137749(n)
%Y A137737 Cf. A114938, A137729, A137730, A137749
%K A137737 nonn
%O A137737 1,4
%A A137737 _Max Alekseyev_, Feb 09 2008