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%I #19 Dec 07 2019 12:18:18
%S 1,547,448540,315323620,232740363922,168973319623174,
%T 123350523324917020,89881489830655851460,65533580739687859229563,
%U 47771556642163840723529281,34826053765400471578213696840
%N Gaussian binomial coefficient [ n,6 ] for q = -3.
%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="/A015324/b015324.txt">Table of n, a(n) for n = 6..200</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (547,149331,-11711817,-316219059,2939282073,7848852129,-10460353203).
%F G.f.: x^6 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(3*x+1)*(243*x+1) ). - _R. J. Mathar_, Aug 04 2016
%t Table[QBinomial[n, 6, -3], {n, 6, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)
%o (Sage) [gaussian_binomial(n,6,-3) for n in range(6,17)] # _Zerinvary Lajos_, May 27 2009
%K nonn,easy
%O 6,2
%A _Olivier Gérard_, Dec 11 1999
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