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).

0, 3, 150, 31185, 12999420, 9622703475, 11539805487210, 20981809690466625, 54997428661808232600, 199760599884519009411075, 973866344327734952575230750, 6207575427404936259602204502225

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

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

Prog

(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) ) ) }

Crossrefs

Cf. A094047, A137801.

Sequence in context: A111816 A157555 A157578 * A100203 A287319 A189248

Adjacent sequences: A137799 A137800 A137801 * A137803 A137804 A137805

Keyword

nonn

Author

Max Alekseyev, Feb 10 2008

Status

approved