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Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal.
6

%I #17 Oct 30 2023 09:44:39

%S 1,2,12,2520,7015680,1395793843200,20278935204394809600,

%T 33190120270913939567661168000

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

%F 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.

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

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

%K nonn,more

%O 1,2

%A _Max Alekseyev_, Aug 24 2022