A256070 Number of inequivalent n X n matrices with entry set {1,...,n}, where equivalence means permutations of rows or columns.

1, 1, 5, 633, 7520386, 20435529209470, 19740907671252532135134, 10077866175951324796988844418739012, 3855174405512686506030123555473042980898031518176, 1492231601551989489818761885384738502799149242563553845787532236092

Offset: 0

Author

Alois P. Heinz, Mar 13 2015

Keywords

• nonn

Examples

			a(2) = 5:
   [1 1]  [1 2]  [1 2]  [1 1]  [1 2]
   [1 2]  [2 2]  [1 2]  [2 2]  [2 1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20
• Index to number of inequivalent matrices modulo permutation of rows and columns

Crossrefs

Main diagonal of A256069.

Programs

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:
a:= n-> add(A(n, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..10);

Formula

a(n) = Sum_{i=0..n} (-1)^i * C(n,i) * A246106(n,n-i).