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%I #23 Sep 08 2022 08:45:49
%S 0,1,288,10206,133120,984375,5062176,20235628,67239936,193975965,
%T 500500000,1179859626,2581383168,5304663091,10334288160,19227375000,
%U 34368126976,59306007033,99196651296,161367371830,256032000000,397182906351,603691298848,900650348676
%N a(n) = n^6*(n^3 + 1)/2.
%C a(n) is the number of inequivalent 3 X 3 matrices with entries in {1,2,...,n} when a matrix and its transpose are considered equivalent. - _Geoffrey Critzer_, Dec 18 2011.
%H Vincenzo Librandi, <a href="/A168555/b168555.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F G.f.: x*(1 + 278*x + 7371*x^2 + 43900*x^3 + 78095*x^4 + 44334*x^5 + 7237*x^6 + 224*x^7) / (1 - x)^10. - _Colin Barker_, Feb 23 2017
%t Table[n^6*(n^3 + 1)/2, {n,0,25}] (* _G. C. Greubel_, Jul 26 2016 *)
%o (Magma) [n^6*(n^3+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 29 2011
%o (PARI) a(n) = (n^6+n^9)/2 \\ _Charles R Greathouse IV_, Dec 20 2011
%o (PARI) concat(0, Vec(x*(1 + 278*x + 7371*x^2 + 43900*x^3 + 78095*x^4 + 44334*x^5 + 7237*x^6 + 224*x^7) / (1 - x)^10 + O(x^30))) \\ _Colin Barker_, Feb 23 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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