A246107 Number of inequivalent n X n matrices with entries from [n], where equivalence means permutations of rows or columns.

1, 1, 7, 738, 7880456, 20834113243925, 19909522361922032493690, 10114980502439545115146468340980932, 3861175753082201291221743022346066208381644388448, 1493197587365241166689220567691206411606485768307602552950789523519

Offset: 0

Author

Alois P. Heinz, Aug 13 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..26
• Index to number of inequivalent matrices modulo permutation of rows and columns

Crossrefs

Main diagonal of A246106.

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-> A(n$2):
seq(a(n), n=0..12);

Formula

a(n) = A246106(2n,n).