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%I #27 Sep 08 2022 08:45:49
%S 0,1,33280,21552885,2148007936,76298828125,1410585186816,
%T 16616606522425,140738025226240,926511837818121,5000005000000000,
%U 22974877900498381,92442160406200320,332708373520835845,1088976813532013056
%N a(n) = n^10*(n^6 + 1)/2.
%C a(n) is number of distinct 4 X 4 matrices with entries in {1,2,...,n} when a matrix and its transpose are considered equivalent. - _David Nacin_, Feb 20 2017
%C Cycle index of this S2 group action is (s(2)^6s(1)^4+s(1)^16)/2. - _David Nacin_, Feb 20 2017
%H Vincenzo Librandi, <a href="/A170798/b170798.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F G.f.: x*(x+1)*(x^14 + 33262*x^13 + 20953999*x^12 + 1765180292*x^11 + 40926077261*x^10 + 350131349138*x^9 + 1253612167971*x^8 + 1937785948152*x^7 + 1253612167971*x^6 + 350131349138*x^5 + 40926077261*x^4 + 1765180292*x^3 + 20953999*x^2 + 33262*x + 1)/(1-x)^17. - _Colin Barker_, Jul 11 2015
%F E.g.f.: x*(2 + 33278*x + 7151016*x^2 + 171833006*x^3 + 1096233075*x^4 + 2734949385*x^5 + 3281888484*x^6 + 2141764803*x^7 + 820784295*x^8 + 193754991*x^9 + 28936908*x^10 + 2757118*x^11 + 165620*x^12 + 6020*x^13 + 120*x^14 + x^15)*exp(x)/2. - _G. C. Greubel_, Oct 12 2019
%e a(2) = 33280 is the number of inequivalent 4 X 4 binary matrices up to taking the transpose. - _David Nacin_, Feb 20 2017
%p seq(n^10*(n^6+1)/2, n=0..20); # _G. C. Greubel_, Oct 12 2019
%t Table[n^10*(n^6+1)/2,{n,0,30}] (* _Harvey P. Dale_, Aug 27 2016 *)
%o (Magma) [n^10*(n^6+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 27 2011
%o (PARI) concat(0, Vec(-x*(x +1)*(x^14 +33262*x^13 +20953999*x^12 +1765180292*x^11 +40926077261*x^10 +350131349138*x^9 +1253612167971*x^8 +1937785948152*x^7 +1253612167971*x^6 +350131349138*x^5 +40926077261*x^4 +1765180292*x^3 +20953999*x^2 +33262*x +1) / (x -1)^17 + O(x^30))) \\ _Colin Barker_, Jul 11 2015
%o (PARI) vector(21, m, (m-1)^10*((m-1)^6 + 1)/2) \\ _G. C. Greubel_, Oct 11 2019
%o (Sage) [n^10*(n^6 +1)/2 for n in (0..20)] # _G. C. Greubel_, Oct 11 2019
%o (GAP) List([0..20], n-> n^10*(n^6 +1)/2); # _G. C. Greubel_, Oct 11 2019
%Y Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), this sequence (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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