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%I #20 Sep 08 2022 08:44:40
%S 1,2876892678661,9104162632986302495960347,
%T 28551311330859170052594978984538703567,
%U 89612366318560505321323986969057938917191132920348,281240247078624326614268823428029385995576471270476701478391628
%N Gaussian binomial coefficient [ n,12 ] for q=-11.
%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="/A015434/b015434.txt">Table of n, a(n) for n = 12..90</a>
%F a(n) = product(((-11)^(n-i+1)-1)/((-11)^i-1), i=1..12) (by definition). - _Vincenzo Librandi_, Nov 06 2012
%t Table[QBinomial[n, 12, -11], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)
%o (Sage) [gaussian_binomial(n,12,-11) for n in range(12,17)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=12; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012
%K nonn,easy
%O 12,2
%A _Olivier Gérard_, Dec 11 1999
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