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A321586
Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows (or distinct columns).
5
1, 1, 4, 26, 204, 1992, 23336, 318080, 4948552, 86550424, 1681106080, 35904872576, 836339613984, 21100105791936, 573194015723840, 16681174764033728, 517768654898701120, 17074080118403865856, 596117945858272441408, 21967609729338776864384, 852095613819396775627200
OFFSET
0,3
LINKS
EXAMPLE
The a(3) = 26 matrices:
[3][21][12][111]
.
[2][20][11][11][110][101][1][10][10][100][02][011][01][01][010][001]
[1][01][10][01][001][010][2][11][02][011][10][100][20][11][101][110]
.
[100][100][010][010][001][001]
[010][001][100][001][100][010]
[001][010][001][100][010][100]
MAPLE
C:= binomial:
b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
b(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k+i-1, i), j), j=0..n/i)))
end:
a:= n-> add(add(b(n$2, i, 0)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):
seq(a(n), n=0..21); # Alois P. Heinz, Sep 16 2019
MATHEMATICA
multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];
prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];
Table[Length[Select[multsubs[Tuples[Range[n], 2], n], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], UnsameQ@@prs2mat[#]]&]], {n, 5}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 13 2018
EXTENSIONS
a(7)-a(20) from Alois P. Heinz, Sep 16 2019
STATUS
approved