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.

1, 0, 2, 4, 38, 330, 7327, 263848, 24102073, 3969532348, 1768504120142, 1428017372007318, 3349182395457443944, 13899438205355143982866, 180235866007281722773278406, 3972621836515553695919909310846

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Example

The a(2) = 2 matrices are the 1 X 1 matrices whose only value is 1 or 2.
The a(3) = 4 matrices are either 1 X 2 or 2 X 1:
    [1]  [1]   [1 1]   [1 2]
    [1]  [2]

Crossrefs

Main diagonal of A397922.

Cf. A397927 (permutations counted separately).

Sequence in context: A396475 A012433 A012438 * A009626 A009835 A362411

Adjacent sequences: A397918 A397919 A397922 * A397924 A397925 A397926

Keyword

nonn,new

Author

Andrew Howroyd, Jul 15 2026

Status

approved