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%I #21 Sep 08 2022 08:44:39
%S 1,-341,232903,-105970865,57881286463,-28735427761313,
%T 14946527496991519,-7593183562134412385,3902985682508407194271,
%U -1994425683761796076272481,1022146087305755916943130783,-523082886040328458081329117025
%N Gaussian binomial coefficient [ n,9 ] for q=-2.
%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="/A015371/b015371.txt">Table of n, a(n) for n = 9..200</a>
%F a(n) = Product_{i=1..9} ((-2)^(n-i+1)-1)/((-2)^i-1). - _Vincenzo Librandi_, Nov 04 2012
%F G.f.: -x^9 / ( (x-1)*(512*x+1)*(64*x-1)*(128*x+1)*(2*x+1)*(8*x+1)*(32*x+1)*(16*x-1)*(4*x-1)*(256*x-1) ). - _R. J. Mathar_, Sep 02 2016
%t Table[QBinomial[n, 9, -2],{n, 9, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o (Sage) [gaussian_binomial(n,9,-2) for n in range(9,21)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=9; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 2012
%Y Diagonal k=9 of the triangular array A015109. See there for further references and programs. - _M. F. Hasler_, Nov 04 2012
%Y Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015375, A015376, A015377, 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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