A137801 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	LINKS	`Proof of the formula (in Russian).`
	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 (maxale(AT)gmail.com), Nov 03 2008]`
	PROG	`(PARI) { a(n) = n! * sum(i=0, n, (-1)^i * sum(j=0, n-i, (2n)! (2n-i-2j)! / (n-i-j)! / i! / j! / 2^(2n-2i-j) ) ) }`
	CROSSREFS	`Cf. A094047, A137802.` `Sequence in context: A078927 A064430 A180992 * A076667 A000652 A175554` `Adjacent sequences: A137798 A137799 A137800 * A137802 A137803 A137804`
	KEYWORD	`nonn`
	AUTHOR	`Max Alekseyev (maxale(AT)gmail.com), Feb 10 2008`

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Last modified February 12 15:29 EST 2012. Contains 205429 sequences.