A357767 Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows.

1, 1, 2, 102, 56904, 1926158520, 4018159809614880, 822978002850717919227120

Offset

1,3

Links

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

Formula

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

a(n) = A357766(n) / n!.

Crossrefs

Cf. A356722, A356723, A356724, A356725, A357766, A357768.

Sequence in context: A202740 A283624 A055693 * A215964 A106299 A176933

Adjacent sequences: A357764 A357765 A357766 * A357768 A357769 A357770

Keyword

hard,more,nonn

Author

Max Alekseyev, Oct 12 2022

Status

approved