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%I #9 May 02 2022 10:25:01
%S 0,1,21467043671008,3379836486315342147630795474,
%T 44407122853769773657258254744483639216,
%U 3140944762272022074073055438393255181867210010,8141947887028911666338424253996955242756334258901612,2154844572709712035236045223460733805672731741592666006584
%N Number of inequivalent 9 X 9 matrices with entries from [n], where equivalence means permutations of rows or columns.
%H Alois P. Heinz, <a href="/A246110/b246110.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) = 1/9!^2*(n+1)*(n^78 -n^77 +n^76 -n^75 +n^74 -n^73 +n^72 -n^71 +n^70 +71*n^69 -71*n^68 +71*n^67 -71*n^66 +71*n^65 -71*n^64 +71*n^63 +1225*n^62 -1225*n^61 +2317*n^60 -2317*n^59 +2317*n^58 -2317*n^57 +2317*n^56 +24899*n^55 -24899*n^54 +36995*n^53 -36995*n^52 +46067*n^51 +96817*n^50 -96817*n^49 +215761*n^48 -215761*n^47 +578641*n^46 +373919*n^45 -373919*n^44 +373919*n^43 +1258579*n^42 +2132837*n^41 -1418417*n^40 +5565833*n^39 -4672808*n^38 +5132456*n^37 +22604680*n^36 -22604680*n^35 +28955080*n^34 +9281888*n^33 +416080*n^32 +82721240*n^31 -4081112*n^30 +83196512*n^29 +31110688*n^28 +59573024*n^27 +195332032*n^26 +91875392*n^25 +409591656*n^24 -42883272*n^23 +575364312*n^22 +674367624*n^21 -304425072*n^20 +1666585872*n^19 +1102868928*n^18 +248242176*n^17 +2588354496*n^16 +1758259872*n^15 +1971980640*n^14 +1000550880*n^13 +4876228512*n^12 +2146207104*n^11 +3236029056*n^10 +6704363520*n^9 +1965067776*n^8 +2962552320*n^7 +12255909120*n^6 -2340576000*n^5 +4626720000*n^4 +7583466240*n^3 +5852528640*n^2 -3474938880*n +7211151360)*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(9):
%p seq(a(n), n=0..10);
%Y Row n=9 of A246106.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 13 2014
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