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%I #19 Sep 08 2022 08:44:40
%S 1,-685853880635,513158776998704708174485,
%T -381060745537275503024171826161834795,
%U 283144978428780810444903027180667803787005364693,-210378243627879792478862753186483140572522717247026752860715
%N Gaussian binomial coefficient [ n,11 ] for q=-12.
%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="/A015421/b015421.txt">Table of n, a(n) for n = 11..90</a>
%F a(n) = Product_{i=1..11} ((-12)^(n-i+1)-1)/((-12)^i-1)). - _Vincenzo Librandi_, Nov 06 2012
%t Table[QBinomial[n, 11, -12], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)
%o (Sage) [gaussian_binomial(n,11,-12) for n in range(11,16)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=11; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012
%K sign,easy
%O 11,2
%A _Olivier Gérard_
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