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%I #25 Sep 08 2022 08:44:39
%S 1,5905,39226915,257015284435,1686534296462470,11065164158125239526,
%T 72598678627860564552010,476319830905927777714449130,
%U 3125134483161392104770081009295,20504007291105533368839949866598015
%N Gaussian binomial coefficient [ n,4 ] 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 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%H Vincenzo Librandi, <a href="/A015295/b015295.txt">Table of n, a(n) for n = 4..200</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5905,4357890,-352989090,-3138159105,3486784401)
%F G.f.: -x^4 / ( (x-1)*(81*x-1)*(9*x+1)*(729*x+1)*(6561*x-1) ). - _R. J. Mathar_, Aug 03 2016
%t Table[QBinomial[n, 4, -9], {n, 4, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o (Sage) [gaussian_binomial(n,4,-9) for n in range(4,14)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=4; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%K nonn,easy
%O 4,2
%A _Olivier Gérard_, Dec 11 1999
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