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%I #19 Sep 08 2022 08:44:39
%S 1,38742049,1688564650965445,72587599955185580267365,
%T 3125134483161392104770081009295,
%U 134524513999723596604019036560420619887,5790850118312580284352508983888376537699322083
%N Gaussian binomial coefficient [ n,8 ] for q=-9.
%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="/A015365/b015365.txt">Table of n, a(n) for n = 8..140</a>
%F a(n) = Product_{i=1..8} ((-9)^(n-i+1)-1)/((-9)^i-1). - _M. F. Hasler_, Nov 03 2012
%t Table[QBinomial[n, 8, -9], {n, 8, 15}] (* _Vincenzo Librandi_, Nov 03 2012 *)
%o (Sage) [gaussian_binomial(n,8,-9) for n in range(8,14)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=8; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // _Vincenzo Librandi_, Nov 03 2012
%o (PARI) A015365(n, r=8, q=-9)=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, A015367, A015368, A015369, A015370. - _M. F. Hasler_, Nov 03 2012
%K nonn,easy
%O 8,2
%A _Olivier Gérard_
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