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%I #22 Sep 08 2022 08:44:39
%S 1,-1627604,3311368882921,-6416187820400919704,
%T 12551699566292514833249671,-24507195908707737696414306347204,
%U 47868680606322065338648160779243199671,-93492320106912696270274007078334075223284704
%N Gaussian binomial coefficient [ n,9 ] 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="/A015377/b015377.txt">Table of n, a(n) for n = 9..170</a>
%F a(n) = Product_{i=1..9} ((-5)^(n-i+1)-1)/((-5)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012
%t Table[QBinomial[n, 9, -5], {n, 9, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o (Sage) [gaussian_binomial(n,9,-5) for n in range(9,16)] # _Zerinvary Lajos_, May 25 2009]
%o (Magma) r:=9; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 2012
%Y Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015375, A015376, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - _Vincenzo Librandi_, Nov 04 2012
%K sign,easy
%O 9,2
%A _Olivier Gérard_
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