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%I #24 Apr 29 2022 18:32:38
%S 1,-104,13546,-1679704,210302171,-26279294704,3285123767796,
%T -410635172794704,51329529054158421,-6416187820400919704,
%U 802023560334345174046,-100252942972187432169704
%N Gaussian binomial coefficient [ n,3 ] 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="/A015272/b015272.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 (-104,2730,13000,-15625).
%F G.f.: x^3/((1-x)*(1+5*x)*(1-25*x)*(1+125*x)). - _Bruno Berselli_, Oct 29 2012
%F a(n) = (-1 + 21*5^(2n-3) + (-1)^n*5^(n-2)*(21-5^(2n-1)))/18144. - _Bruno Berselli_, Oct 29 2012
%t Table[QBinomial[n, 3, -5], {n, 3, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%t LinearRecurrence[{-104,2730,13000,-15625},{1,-104,13546,-1679704},20] (* _Harvey P. Dale_, Apr 29 2022 *)
%o (Sage) [gaussian_binomial(n,3,-5) for n in range(3,15)] # _Zerinvary Lajos_, May 27 2009
%K sign,easy
%O 3,2
%A _Olivier Gérard_, Dec 11 1999
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