A035482 Number of n X n symmetric matrices each of whose rows is a permutation of 1..n.

1, 1, 2, 6, 96, 720, 328320, 31449600, 440952422400, 444733651353600, 471835793808949248000, 10070314878246926155776000, 1058410183156945383046388908032000, 614972203951464612786852376432607232000

Offset: 0

Author

Joshua Zucker and Joe Keane

Keywords

• more
• nonn

Comments

The even and odd subsequences are A036980, A036981.

Examples

			a(3) = 6 because the first row is arbitrary (say, 213) and the rest is then determined. By symmetry the second row has to be 132 or 123 but in order for the third row/column to work it has to be 132.
		

Crossrefs

Cf. A000438, A035481, A000315, A002860, A003090, A040082.

Formula

a(n) = A035481(n) * n!. [From Max Alekseyev, Apr 23 2010]

Extensions

a(10)-a(13) (using A035481) from Alois P. Heinz, May 05 2023