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 A137802 Number of arrangements of 2n couples into n cars such that each car contains 2 men and 2 women but no couple (cars are unlabeled). 1

%I

%S 0,3,150,31185,12999420,9622703475,11539805487210,20981809690466625,

%T 54997428661808232600,199760599884519009411075,

%U 973866344327734952575230750,6207575427404936259602204502225

%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 unlabeled).

%F a(n) = A137801(n) / n! = SUM[i+j<=n] (-1)^i * (2n)! * (2n-i-2j)! / (n-i-j)! / i! / j! / 2^(2n-2i-j)

%o (PARI) { a(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, A137801.

%K nonn

%O 1,2

%A _Max Alekseyev_, Feb 10 2008

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Last modified November 26 17:52 EST 2021. Contains 349343 sequences. (Running on oeis4.)