A356722 Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal.

1, 2, 12, 2520, 7015680, 1395793843200, 20278935204394809600, 33190120270913939567661168000

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Formula

a(n) = the coefficient of (x1*...*xn)^(n*(n-1)/2) in (Sum x1^(n-1)*x2^(n-2)*...*xn^0)^n, where the sum is taken over all permutations of the variables x1, ..., xn.

a(n) = A356723(n) * n!.

Crossrefs

Cf. A356723 (up to permutation of columns), A356724 (up to permutation of rows), A356725 (up to permutations of both columns and rows).

Sequence in context: A360067 A357766 A050649 * A357765 A003042 A000887

Adjacent sequences: A356719 A356720 A356721 * A356723 A356724 A356725

Keyword

nonn,more

Author

Max Alekseyev, Aug 24 2022

Status

approved