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%I #6 Mar 30 2012 17:27:00
%S 0,6,900,748440,1559930400,6928346502000,58160619655538400,
%T 845986566719614320000,19957466912796971445888000,
%U 724891264860942581350908960000,38873628093261330554954970801600000
%N Number of arrangements of 2n couples into n cars such that each car contains 2 men and 2 women but no couple (cars are labeled).
%H <a href="http://dxdy.ru/post92408.html#p92408">Proof of the formula</a> (in Russian).
%F a(n) = n! * A137802(n) = n! * SUM[i+j<=n] (-1)^i * (2n)! * (2n-i-2j)! / (n-i-j)! / i! / j! / 2^(2n-2i-j)
%F a(n) = A000459(n) * (2n)! / 2^n = A000316(n) * (2n)! / 4^n [From _Max Alekseyev_, Nov 03 2008]
%o (PARI) { a(n) = n! * sum(i=0,n, (-1)^i * sum(j=0,n-i, (2*n)! * (2*n-i-2*j)! / (n-i-j)! / i! / j! / 2^(2*n-2*i-j) ) ) }
%Y Cf. A094047, A137802.
%K nonn
%O 1,2
%A _Max Alekseyev_, Feb 10 2008
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