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

%I A246107 #13 May 02 2022 10:24:02
%S A246107 1,1,7,738,7880456,20834113243925,19909522361922032493690,
%T A246107 10114980502439545115146468340980932,
%U A246107 3861175753082201291221743022346066208381644388448,1493197587365241166689220567691206411606485768307602552950789523519
%N A246107 Number of inequivalent n X n matrices with entries from [n], where equivalence means permutations of rows or columns.
%H A246107 Alois P. Heinz, <a href="/A246107/b246107.txt">Table of n, a(n) for n = 0..26</a>
%H A246107 <a href="/index/Mat#inequiv">Index to number of inequivalent matrices modulo permutation of rows and columns</a>
%F A246107 a(n) = A246106(2n,n).
%p A246107 b:= proc(n, i) option remember; `if`(n=0, [[]],
%p A246107       `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
%p A246107        b(n-i*j, i-1))[], j=1..n/i)]))
%p A246107     end:
%p A246107 A:= proc(n, k) option remember; add(add(k^add(add(i[2]*j[2]*
%p A246107       igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
%p A246107       /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2))
%p A246107     end:
%p A246107 a:= n-> A(n$2):
%p A246107 seq(a(n), n=0..12);
%Y A246107 Main diagonal of A246106.
%K A246107 nonn
%O A246107 0,3
%A A246107 _Alois P. Heinz_, Aug 13 2014