A397927 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.

1, 0, 2, 6, 122, 3300, 244502, 35533946, 13894204922, 11254924831650, 25931152822648922, 123129026842442598010, 1767099204159492194923140, 50472055186683607738951340430, 4642825806461056714820871058427887, 807990421462131145735305221452897896990

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) = 6 matrices are either 1 X 2 or 2 X 1:
    [1]  [1]  [2]   [1 1]   [1 2]   [2 1]
    [1]  [2]  [1]

Crossrefs

Main diagonal of A397926.

Cf. A397923 (up to row and column permutations).

Sequence in context: A039716 A164955 A060001 * A181316 A101753 A288185

Adjacent sequences: A397924 A397925 A397926 * A397929 A397930 A397931

Keyword

nonn,new

Author

Andrew Howroyd, Jul 16 2026

Status

approved