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A246109 Number of inequivalent 8 X 8 matrices with entries from [n], where equivalence means permutations of rows or columns.

%I A246109 #9 May 02 2022 10:24:42
%S A246109 0,1,14685630688,2130536585704570302966,
%T A246109 209493560585995285291677153144,333504381764054807093590006199733915,
%U A246109 38963096281905114770318673967657388979120,750304814691805977574386038534306614497574954,3861175753082201291221743022346066208381644388448
%N A246109 Number of inequivalent 8 X 8 matrices with entries from [n], where equivalence means permutations of rows or columns.
%H A246109 Alois P. Heinz, <a href="/A246109/b246109.txt">Table of n, a(n) for n = 0..1000</a>
%H A246109 <a href="/index/Mat#inequiv">Index to number of inequivalent matrices modulo permutation of rows and columns</a>
%F A246109 a(n) = 1/8!^2*(n^62 +56*n^54 +784*n^48 +644*n^46 +11760*n^42 +6272*n^40 +48020*n^38 +36064*n^36 +309680*n^34 +176400*n^32 +1060423*n^30 +423360*n^28 +4877264*n^26 +4845120*n^24 +14721560*n^22 +17144512*n^20 +41692336*n^18 +41106688*n^16 +123789552*n^14 +139448064*n^12 +197401344*n^10 +190027776*n^8 +288610560*n^6 +239339520*n^4 +235468800*n^2 +85155840)*n^2.
%p A246109 b:= proc(n, i) option remember; `if`(n=0, [[]],
%p A246109       `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
%p A246109        b(n-i*j, i-1))[], j=1..n/i)]))
%p A246109     end:
%p A246109 a:= proc(n) unapply(add(add(x^add(add(i[2]*j[2]*
%p A246109       igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
%p A246109       /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2)), x)
%p A246109     end(8):
%p A246109 seq(a(n), n=0..10);
%Y A246109 Row n=8 of A246106.
%K A246109 nonn
%O A246109 0,3
%A A246109 _Alois P. Heinz_, Aug 13 2014