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

%I A256070 #13 Feb 28 2023 08:29:14
%S A256070 1,1,5,633,7520386,20435529209470,19740907671252532135134,
%T A256070 10077866175951324796988844418739012,
%U A256070 3855174405512686506030123555473042980898031518176,1492231601551989489818761885384738502799149242563553845787532236092
%N A256070 Number of inequivalent n X n matrices with entry set {1,...,n}, where equivalence means permutations of rows or columns.
%H A256070 Alois P. Heinz, <a href="/A256070/b256070.txt">Table of n, a(n) for n = 0..20</a>
%H A256070 <a href="/index/Mat#inequiv">Index to number of inequivalent matrices modulo permutation of rows and columns</a>
%F A256070 a(n) = Sum_{i=0..n} (-1)^i * C(n,i) * A246106(n,n-i).
%e A256070 a(2) = 5:
%e A256070    [1 1]  [1 2]  [1 2]  [1 1]  [1 2]
%e A256070    [1 2]  [2 2]  [1 2]  [2 2]  [2 1].
%p A256070 b:= proc(n, i) option remember; `if`(n=0, [[]],
%p A256070       `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
%p A256070        b(n-i*j, i-1))[], j=1..n/i)]))
%p A256070     end:
%p A256070 A:= proc(n, k) option remember; add(add(k^add(add(i[2]*j[2]*
%p A256070       igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
%p A256070       /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2))
%p A256070     end:
%p A256070 a:= n-> add(A(n, n-i)*(-1)^i*binomial(n, i), i=0..n):
%p A256070 seq(a(n), n=0..10);
%Y A256070 Main diagonal of A256069.
%K A256070 nonn
%O A256070 0,3
%A A256070 _Alois P. Heinz_, Mar 13 2015