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%I #25 Sep 08 2022 08:44:39
%S 1,-1220,1637362,-2177691460,2898705467483,-3858153003126520,
%T 5135204548028317764,-6834956902420811530200,
%U 9097327679593690752247605,-12108543136400139930131294300,16116470915170412804822871108406
%N Gaussian binomial coefficient [ n,3 ] for q = -11.
%D J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H Vincenzo Librandi, <a href="/A015279/b015279.txt">Table of n, a(n) for n = 3..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1220,148962,1623820,-1771561).
%F a(n) = product(((-11)^(n-i+1)-1)/((-11)^i-1), i=1..3) (by definition). - _Vincenzo Librandi_, Aug 02 2016
%F G.f.: x^3 / ( (x-1)*(11*x+1)*(121*x-1)*(1331*x+1) ). - _R. J. Mathar_, Aug 03 2016
%t Table[QBinomial[n, 3, -11], {n, 3, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o (Sage) [gaussian_binomial(n,3,-11) for n in range(3,14)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=3; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%K sign,easy
%O 3,2
%A _Olivier Gérard_, Dec 11 1999
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