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%I #10 May 02 2022 10:24:21
%S 0,1,33642660,9610448114487414,12508419942924578958856,
%T 699686291478538604891895515,5304145637506715118807098435916,
%U 10114980502439545115146468340980932,7023555040334136447558331379882184096,2254372634250117773973027448098778962279
%N Number of inequivalent 7 X 7 matrices with entries from [n], where equivalence means permutations of rows or columns.
%H Alois P. Heinz, <a href="/A246108/b246108.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mat#inequiv">Index to number of inequivalent matrices modulo permutation of rows and columns</a>
%F a(n) = 1/7!^2*(n+1)*(n^46 -n^45 +n^44 -n^43 +n^42 -n^41 +n^40 +41*n^39 -41*n^38 +41*n^37 -41*n^36 +41*n^35 +400*n^34 -400*n^33 +750*n^32 -750*n^31 +750*n^30 +3660*n^29 -3660*n^28 +6600*n^27 +4425*n^26 -2955*n^25 +12265*n^24 +9785*n^23 +42400*n^22 -42400*n^21 +42400*n^20 +148700*n^19 -145452*n^18 +224832*n^17 +343568*n^16 -134240*n^15 +418440*n^14 +257760*n^13 +506640*n^12 +114288*n^11 +596016*n^10 +868104*n^9 +737136*n^8 +1605456*n^7 +2000160*n^6 -95040*n^5 +1320480*n^4 +262080*n^3 +1260000*n^2 -201600*n +2540160)*n^2.
%p b:= proc(n, i) option remember; `if`(n=0, [[]],
%p `if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
%p b(n-i*j, i-1))[], j=1..n/i)]))
%p end:
%p a:= proc(n) unapply(add(add(x^add(add(i[2]*j[2]*
%p igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
%p /mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2)), x)
%p end(7):
%p seq(a(n), n=0..10);
%Y Row n=7 of A246106.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 13 2014
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