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

0,3

Comments

The even and odd subsequences are A036980, A036981.

Links

Table of n, a(n) for n=0..13.

Formula

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

Example

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.

Sequence in context: A280117 A129364 A092287 * A322716 A372240 A007870

Adjacent sequences: A035479 A035480 A035481 * A035483 A035484 A035485

Keyword

more,nonn

Author

Joshua Zucker and Joe Keane

Extensions

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

Status

approved