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A246106 Number A(n,k) of inequivalent n X n matrices with entries from [k], where equivalence means permutations of rows or columns; square array A(n,k), n>=0, k>=0, read by antidiagonals. 26
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 7, 1, 0, 1, 4, 27, 36, 1, 0, 1, 5, 76, 738, 317, 1, 0, 1, 6, 175, 8240, 90492, 5624, 1, 0, 1, 7, 351, 57675, 7880456, 64796982, 251610, 1, 0, 1, 8, 637, 289716, 270656150, 79846389608, 302752867740, 33642660, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Antidiagonals n = 0..27, flattened

FORMULA

A(n,k) = Sum_{i=0..k} C(k,i) * A256069(n,i).

EXAMPLE

Square array A(n,k) begins:

  1, 1,    1,        1,           1,              1, ...

  0, 1,    2,        3,           4,              5, ...

  0, 1,    7,       27,          76,            175, ...

  0, 1,   36,      738,        8240,          57675, ...

  0, 1,  317,    90492,     7880456,      270656150, ...

  0, 1, 5624, 64796982, 79846389608, 20834113243925, ...

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [[]],

      `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],

       b(n-i*j, i-1))[], j=1..n/i)]))

    end:

A:= proc(n, k) option remember; add(add(k^add(add(i[2]*j[2]*

      igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)

      /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2))

    end:

seq(seq(A(n, d-n), n=0..d), d=0..10);

CROSSREFS

Columns k=0-10 give: A000007, A000012, A002724, A052269, A052271, A052272, A246112, A246113, A246114, A246115, A246116.

Rows n=0-10 give: A000012, A001477, A039623, A058001, A058002, A058003, A058004, A246108, A246109, A246110, A246111.

Main diagonal gives A246107.

A028657 is a very similar array.

Cf. A242095, A256069.

Sequence in context: A322280 A210472 A320080 * A322836 A305466 A160114

Adjacent sequences:  A246103 A246104 A246105 * A246107 A246108 A246109

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Aug 13 2014

STATUS

approved

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Last modified May 25 01:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)