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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

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

Cf. A007716, A049311, A101370, A120733, A283877, A316980, A321446, A321587.

Row sums of A327245.

Sequence in context: A141381 A118971 A124554 * A206391 A228966 A291533

Adjacent sequences:  A321583 A321584 A321585 * A321587 A321588 A321589

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 13 2018

EXTENSIONS

a(7)-a(20) from Alois P. Heinz, Sep 16 2019

STATUS

approved

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Last modified August 11 00:32 EDT 2020. Contains 336403 sequences. (Running on oeis4.)