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%I #18 Sep 08 2022 08:44:40
%S 1,-261535698060,75241013495730790109766,
%T -21451022788016578429723510655178620,
%U 6120645196266098901030880937026524413510456541,-1746280663134874755499501790878094901668461626016352027280
%N Gaussian binomial coefficient [ n,11 ] 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="/A015418/b015418.txt">Table of n, a(n) for n = 11..90</a>
%F a(n) = Product_{i=1..11} ((-11)^(n-i+1)-1)/((-11)^i-1). - _Vincenzo Librandi_, Nov 06 2012
%t Table[QBinomial[n, 11, -11], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)
%o (Sage) [gaussian_binomial(n,11,-11) for n in range(11,16)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=11; q:=-11; [&*[(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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