%I #26 Sep 08 2022 08:44:39
%S 1,-2604,8476671,-26279294704,82254445109046,-256962886520659704,
%T 803060432690378496546,-2509531719872244898534704,
%U 7842306707330337276457324671,-24507195908707737696414306347204
%N Gaussian binomial coefficient [ n,5 ] for q = -5.
%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="/A015309/b015309.txt">Table of n, a(n) for n = 5..200</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-2604,1695855,209963000,-5299546875,-25429687500,30517578125)
%F G.f.: -x^5 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(125*x+1)*(3125*x+1) ). - _R. J. Mathar_, Aug 04 2016
%t Table[QBinomial[n, 5, -5], {n, 5, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o (Sage) [gaussian_binomial(n,5,-5) for n in range(5,15)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=5; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Aug 03 2016
%K sign,easy
%O 5,2
%A _Olivier GĂ©rard_, Dec 11 1999