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Gaussian binomial coefficient [ n,9 ] for q=-7.
13

%I #17 Sep 08 2022 08:44:39

%S 1,-35309406,1454546516636543,-58525570007342935110900,

%T 2362701900656492615160524472603,

%U -95337871447349860183019420430515900118,3847259697771549596318959641032366290112134229

%N Gaussian binomial coefficient [ n,9 ] 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="/A015379/b015379.txt">Table of n, a(n) for n = 9..140</a>

%F a(n) = Product_{i=1..9} ((-7)^(n-i+1)-1)/((-7)^i-1). - _Vincenzo Librandi_, Nov 04 2012

%t Table[QBinomial[n, 9, -7],{n, 9, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)

%o (Sage) [gaussian_binomial(n,9,-7) for n in range(9,15)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=9; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 2012

%Y Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13: A015371, A015375, A015376, A015377, A015378, A015380, A015381, A015382, A015383, A015384, A015385. - _Vincenzo Librandi_, Nov 04 2012

%K sign,easy

%O 9,2

%A _Olivier GĂ©rard_