A137801 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).

0, 6, 900, 748440, 1559930400, 6928346502000, 58160619655538400, 845986566719614320000, 19957466912796971445888000, 724891264860942581350908960000, 38873628093261330554954970801600000

Offset: 1

Author

Max Alekseyev, Feb 10 2008

Keywords

• nonn

Links

• Proof of the formula (in Russian).

Crossrefs

Cf. A094047, A137802.

Programs

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) ) ) }

Formula

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)

a(n) = A000459(n) * (2n)! / 2^n = A000316(n) * (2n)! / 4^n [From Max Alekseyev, Nov 03 2008]