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Gaussian binomial coefficient [ n,7 ] for q = -6.
2

%I #20 Sep 08 2022 08:44:39

%S 1,-239945,69088371619,-19251196169490725,5393264335151280477835,

%T -1509574711680960125598763925,422593364163884169440003098013995,

%U -118298673397216914972187267242547690325,33116077152651051199781730118147946460139435

%N Gaussian binomial coefficient [ n,7 ] for q = -6.

%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="/A015345/b015345.txt">Table of n, a(n) for n = 7..190</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-239945,11514768594,89124308917560,-115609163009731776,-24949102541146076160,902345215627683201024,5263661621405464657920,-6140942214464815497216)

%F G.f.: x^7 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1) ). - _R. J. Mathar_, Sep 02 2016

%t Table[QBinomial[n, 7, -6], {n, 7, 20}] (* _Vincenzo Librandi_, Nov 02 2012 *)

%o (Sage) [gaussian_binomial(n,7,-6) for n in range(7,15)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=7; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // _Vincenzo Librandi_, Nov 02 2012

%K sign,easy

%O 7,2

%A _Olivier GĂ©rard_, Dec 11 1999