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%I #19 Dec 07 2019 12:18:18
%S 1,-53144,3177326971,-187360965026144,11065164158125239526,
%T -653375813208979143531248,38581260992855637306941215162,
%U -2278184404047301621409794099651808
%N Gaussian binomial coefficient [ n,5 ] for q = -9.
%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="/A015315/b015315.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 (-53144,353042235,256976057520,-20846790934515,-185301670206744,205891132094649).
%F G.f.: -x^5 / ( (x-1)*(81*x-1)*(9*x+1)*(729*x+1)*(6561*x-1)*(59049*x+1) ). - _R. J. Mathar_, Aug 04 2016
%t Table[QBinomial[n, 5, -9], {n, 5, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o (Sage) [gaussian_binomial(n,5,-9) for n in range(5,13)] # _Zerinvary Lajos_, May 27 2009
%K sign,easy
%O 5,2
%A _Olivier Gérard_, Dec 11 1999
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