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%I #27 May 01 2022 02:08:12
%S 1,3,27,738,90492,64796982,302752867740,9610448114487414,
%T 2130536585704570302966,3379836486315342147630795474,
%U 39197947672609240635681299333726499,3385559039111928075792568062997302563515455,2212558055097091715366351569353345370930731329332056
%N Number of n X n matrices over GF(3) up to row and column permutations.
%H Alois P. Heinz, <a href="/A052269/b052269.txt">Table of n, a(n) for n = 0..26</a>
%H <a href="/index/Mat#inequiv">OEIS Index to number of inequivalent matrices modulo permutation of row and columns</a>.
%F a(n) = Sum_{1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n} (fixA[s_1, s_2, ...;t_1, t_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!*...)) where fixA[...] = 3^Sum_{i, j>=1} (gcd(i,j)*s_i*t_j). - _Christian G. Bower_, Dec 18 2003
%o (PARI) A052269(n)=A353585(3,n,n) \\ _M. F. Hasler_, Apr 30 2022
%Y Cf. A002724, A052271, A052272, A091060.
%Y Column k=3 of A246106.
%K nonn
%O 0,2
%A _Vladeta Jovovic_, Feb 04 2000
%E More terms from _Alois P. Heinz_, Jul 31 2014
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