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%I #21 Sep 08 2022 08:44:39
%S 1,9090909091,91827364555463728191,917356289265463645628926537191,
%T 9174480340688613582018540679613398447191,
%U 91743885968026547299515818524084563811678679347191,917439777120042501293773510987809326410294679682025870347191
%N Gaussian binomial coefficient [ n,10 ] for q=-10.
%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="/A015398/b015398.txt">Table of n, a(n) for n = 10..110</a>
%F a(n) = Product_{i=1..10} ((-10)^(n-i+1)-1)/((-10)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012
%t Table[QBinomial[n, 10, -10], {n, 10, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o (Sage) [gaussian_binomial(n,10,-10) for n in range(10,16)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=10; q:=-10; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 04 2012
%Y Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015399, A015401, A015402. - _Vincenzo Librandi_, Nov 04 2012
%K nonn,easy
%O 10,2
%A _Olivier Gérard_
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