A397923 - OEIS

A397923

Number of nonnegative integer matrices with a total of n rows and columns with each row sum and column sum nonzero and at most n, up to permutations of rows and columns.

%I #7 Jul 18 2026 21:29:51

%S 1,0,2,4,38,330,7327,263848,24102073,3969532348,1768504120142,

%T 1428017372007318,3349182395457443944,13899438205355143982866,

%U 180235866007281722773278406,3972621836515553695919909310846

%N Number of nonnegative integer matrices with a total of n rows and columns with each row sum and column sum nonzero and at most n, up to permutations of rows and columns.

%e The a(2) = 2 matrices are the 1 X 1 matrices whose only value is 1 or 2.

%e The a(3) = 4 matrices are either 1 X 2 or 2 X 1:

%e [1] [1] [1 1] [1 2]

%e [1] [2]

%Y Main diagonal of A397922.

%Y Cf. A397927 (permutations counted separately).

%K nonn,new

%O 0,3

%A _Andrew Howroyd_, Jul 15 2026