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 A015399 Gaussian binomial coefficient [ n,10 ] for q=-11. 12

%I

%S 1,23775972551,621826557818118395106,16116470915170412804822871108406,

%T 418048302457998082359053173653182700919721,

%U 10843028997901257369999365975865569183708813670389271

%N Gaussian binomial coefficient [ n,10 ] 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="/A015399/b015399.txt">Table of n, a(n) for n = 10..100</a>

%F a(n) = Product_{i=1..10} ((-11)^(n-i+1)-1)/((-11)^i-1) (by definition). - _Vincenzo Librandi_, Nov 05 2012

%t Table[QBinomial[n, 10, -11], {n, 10, 20}] (* _Vincenzo Librandi_, Nov 05 2012 *)

%o (Sage) [gaussian_binomial(n,10,-11) for n in range(10,16)] # _Zerinvary Lajos_, May 25 2009

%o (MAGMA) r:=10; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 05 2012

%Y Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015401, A015402.

%K nonn,easy

%O 10,2