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A015386 Gaussian binomial coefficient [ n,10 ] for q=-2.

%I A015386 #26 Sep 08 2022 08:44:39
%S A015386 1,683,932295,848699215,926949282623,920460637644639,
%T A015386 957498220445101855,972884994173649887135,1000137219716325891620511,
%U A015386 1022146087305755916943130783,1047699739488399814866709052575,1072321450350081081965428740719775
%N A015386 Gaussian binomial coefficient [ n,10 ] for q=-2.
%D A015386 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 A015386 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015386 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015386 Vincenzo Librandi, <a href="/A015386/b015386.txt">Table of n, a(n) for n = 10..200</a>
%H A015386 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (683,465806,-106203768, -14443712448,903388560384,28908433932288,-473291569496064, -3563607111499776,16004972290244608,24030926136672256,-36028797018963968).
%F A015386 a(n) = Product_{i=1..10} ((-2)^(n-i+1)-1)/((-2)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012
%F A015386 G.f.: x^10 / ( (x-1)*(512*x+1)*(64*x-1)*(128*x+1)*(1024*x-1)*(2*x+1)*(8*x+1)*(32*x+1)*(16*x-1)*(4*x-1)*(256*x-1) ). - _R. J. Mathar_, Sep 22 2016
%t A015386 Table[QBinomial[n, 10, -2],{n, 10, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o A015386 (Sage) [gaussian_binomial(n,10,-2) for n in range(10,21)] # _Zerinvary Lajos_, May 25 2009
%o A015386 (Magma) r:=10; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 04 2012
%Y A015386 Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402.
%K A015386 nonn,easy
%O A015386 10,2
%A A015386 _Olivier Gérard_