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 A015344 Gaussian binomial coefficient [ n,7 ] for q = -5. 2

%I

%S 1,-65104,5298179796,-410635172794704,32132285187903171546,

%T -2509531719872244898534704,196069714237340352552410777796,

%U -15317750355077977702804539604534704,1196702310087594273181943625299134137171

%N Gaussian binomial coefficient [ n,7 ] for q = -5.

%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="/A015344/b015344.txt">Table of n, a(n) for n = 7..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-65104,1059648980,3284911838000,-2057018110093750,-256633737343750000,6467584106445312500,31044006347656250000,-37252902984619140625).

%F G.f.: x^7 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(78125*x+1)*(125*x+1)*(15625*x-1)*(3125*x+1) ). - _R. J. Mathar_, Sep 02 2016

%t Table[QBinomial[n, 7, -5], {n, 7, 20}] (* _Vincenzo Librandi_, Nov 02 2012 *)

%o (Sage) [gaussian_binomial(n,7,-5) for n in xrange(7,15)] # _Zerinvary Lajos_, May 27 2009

%o (MAGMA) r:=7; q:=-5; [&*[(1 - q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // _Vincenzo Librandi_, Nov 02 2012

%K sign,easy

%O 7,2

%A _Olivier GĂ©rard_, Dec 11 1999

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Last modified April 22 08:25 EDT 2019. Contains 322329 sequences. (Running on oeis4.)