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Gaussian binomial coefficient [ n,5 ] for q = -10.
4

%I #19 Dec 07 2019 12:18:18

%S 1,-90909,9182728191,-917355454462809,91744720010017447191,

%T -9174380256281734701652809,917438943076290926712489347191,

%U -91743885133148835462057759420652809

%N Gaussian binomial coefficient [ n,5 ] for q = -10.

%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="/A015316/b015316.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 (-90909,918281910,917272809000,-91828191000000,-909090000000000,1000000000000000).

%F G.f.: -x^5 / ( (x-1)*(10*x+1)*(1000*x+1)*(100*x-1)*(10000*x-1)*(100000*x+1) ). - _R. J. Mathar_, Aug 04 2016

%t Table[QBinomial[n, 5, -10], {n, 5, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)

%o (Sage) [gaussian_binomial(n,5,-10) for n in range(5,13)] # _Zerinvary Lajos_, May 27 2009

%K sign,easy

%O 5,2

%A _Olivier GĂ©rard_, Dec 11 1999