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 A015368 Gaussian binomial coefficient [ n,8 ] for q=-11. 13

%I

%S 1,196495641,42471590605551405,9097327679593690752247605,

%T 1950226184559914695131839252162415,

%U 418045706884240723248900544124967821025015,89611860518118688087749643530422009144522097477435

%N Gaussian binomial coefficient [ n,8 ] 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="/A015368/b015368.txt">Table of n, a(n) for n = 8..100</a>

%F a(n) = Product_{i=1..8} ((-11)^(n-i+1)-1)/((-11)^i-1). - _M. F. Hasler_, Nov 03 2012

%t Table[QBinomial[n, 8, -11], {n, 8, 14}] (* _Vincenzo Librandi_, Nov 03 2012 *)

%o (Sage) [gaussian_binomial(n,8,-11) for n in range(8,14)] # _Zerinvary Lajos_, May 25 2009

%o (MAGMA) r:=8; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // _Vincenzo Librandi_, Nov 03 2012

%o (PARI) A015368(n,r=8,q=-11)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ _M. F. Hasler_, Nov 03 2012

%Y Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015369, A015370. - _M. F. Hasler_, Nov 03 2012

%K nonn,easy

%O 8,2