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%I #23 Sep 08 2022 08:44:39
%S 1,838861,938250090141,968690748238618461,1019729183363623510391901,
%T 1068220365220113899181567068253,
%U 1120383768613759382944995805859747933,1174735830441360695151745376566623493806173,1231818594183047090443637654682442929123639613533
%N Gaussian binomial coefficient [ n,10 ] for q=-4.
%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="/A015390/b015390.txt">Table of n, a(n) for n = 10..150</a>
%F a(n) = Product_{i=1..10} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012
%F G.f.: x^10 / ((x-1) * (4*x+1) * (16*x-1) * (64*x+1) * (256*x-1) * (1024*x+1) * (4096*x-1) * (16384*x+1) * (65536*x-1) * (262144*x+1) * (1048576*x-1)). - _Colin Barker_, Jan 13 2014
%t Table[QBinomial[n, 10, -4], {n, 10, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)
%o (Sage) [gaussian_binomial(n,10,-4) for n in range(10,17)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=10; q:=-4; [&*[(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, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402. - _Vincenzo Librandi_, Nov 04 2012
%K nonn,easy
%O 10,2
%A _Olivier Gérard_
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