%I A114939
%S A114939 0,1,7,216,10956,803400,83003040,11579823360,2080493573760,
%T A114939 469031859192960,129727461014726400,43176116371928601600,
%U A114939 17025803126147196057600,7850538273249476117913600
%N A114939 Number of essentially different seating arrangements for n couples around 
               a circular table with 2*n seats avoiding spouses being neighbors 
               and avoiding clusters of 3 persons with equal gender.
%C A114939 Arrangements that differ only by rotation or reflection are excluded 
               by the following conditions: Seat number 1 is assigned to person 
               (a). Person (a)'s spouse (A) can only take seats with numbers <=(n+1). 
               If (A) gets seat n+1 (i.e. sits exactly opposite to her/his spouse) 
               then person (B) can only take seats with numbers <= n.
%F A114939 See PARI code for the formula.
%e A114939 a(2)=1 because the only valid arrangement is aBAb.
%e A114939 a(3)=7 because the only valid arrangements under the given conditions 
               are: abAcBC, aBAcbC, aBcAbC, aBcACb, acAbCB, acBAbC, aCAbcB.
%o A114939 (PARI) { a(n) = if(n<=1, 0, (-1)^n*(n-1)!*2^(n-1) + n! * polcoeff( polcoeff( 
               [0, 2*y*z^3 + z^2, -3*y*z^5 - 4*z^4 + ((-2*y^2 - 1)/y)*z^3, 6*y*z^7 
               + (4*y^2 + 11)*z^6 + ((8*y^2 + 4)/y)*z^5 + 3*z^4] * sum(j=0,n-1, 
               j! * [0, 0, 0, -z^6 + z^4; 1, 0, 0, ((y^2 + 1)/y)*z^5 - 2*z^4 + ((-y^2 
               - 1)/y)*z^3; 0, 1, 0, ((2*y^2 + 2)/y)*z^3 + z^2; 0, 0, 1, -2*z^2]^(n+j) 
               ) * [1,0,0,0]~, 2*n,z), 0,y) / 2 ); }
%Y A114939 Cf. A114938, A137729, A137730, A137737, A137749.
%Y A114939 Sequence in context: A061028 A045760 A046033 this_sequence A145107 A140018 
               A009488
%Y A114939 Adjacent sequences: A114936 A114937 A114938 this_sequence A114940 A114941 
               A114942
%K A114939 nonn
%O A114939 1,3
%A A114939 Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 08 2006
%E A114939 a(4..7) corrected, formula and further term provided by Max Alekseyev 
               (maxale(AT)gmail.com), Feb 15 2008