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Gaussian binomial coefficient [ n,5 ] for q = -7.
4

%I #30 Sep 08 2022 08:44:39

%S 1,-14706,252313293,-4228301370600,71094673339606302,

%T -1194817080145423511412,20081461365765141084602686,

%U -337508711324786004755672161800,5672509895284807570626050787828903

%N Gaussian binomial coefficient [ n,5 ] for q = -7.

%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="/A015312/b015312.txt">Table of n, a(n) for n = 5..100</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-14706,36046857,12322995300,-605839525599,-4154081011794,4747561509943).

%F G.f.: -x^5 / ( (x-1)*(16807*x+1)*(49*x-1)*(343*x+1)*(7*x+1)*(2401*x-1) ). - _R. J. Mathar_, Aug 04 2016

%t QBinomial[Range[5,20],5,-7] (* _Harvey P. Dale_, Feb 27 2012 *)

%o (Sage) [gaussian_binomial(n,5,-7) for n in range(5,14)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=5; q:=-7; [&*[(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