%I #19 Sep 08 2022 08:44:39
%S 1,-3355443,15011998086813,-61996192875273494691,
%T 261050608944894743386831965,-1093857392934787687867181291059107,
%U 4589090822384565497755014953620236474461,-19246867256860431244800698494652605702283863971
%N Gaussian binomial coefficient [ n,11 ] for q=-4.
%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="/A015408/b015408.txt">Table of n, a(n) for n = 11..150</a>
%F a(n) = Product_{i=1..11} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - _Vincenzo Librandi_, Nov 05 2012
%t Table[QBinomial[n, 11, -4], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 05 2012 *)
%o (Sage) [gaussian_binomial(n,11,-4) for n in range(11,18)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=11; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 05 2012
%K sign,easy
%O 11,2
%A _Olivier GĂ©rard_