A015376 - OEIS

%I #21 Sep 08 2022 08:44:39

%S 1,-209715,58640578205,-15135778281070755,3983313338565919030365,

%T -1043182954580986851130914723,273530932713230996784935699290205,

%U -71700116580663579186545558567554787235,18796042166858164201094703719132482337953885

%N Gaussian binomial coefficient [ n,9 ] 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="/A015376/b015376.txt">Table of n, a(n) for n = 9..190</a>

%F a(n) = Product_{i=1..9} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012

%F G.f.: -x^9 / ( (x-1)*(16384*x+1)*(4096*x-1)*(256*x-1)*(65536*x-1)*(64*x+1)*(262144*x+1)*(4*x+1)*(16*x-1)*(1024*x+1) ). - _R. J. Mathar_, Sep 02 2016

%t Table[QBinomial[n, 9, -4],{n, 9, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)

%o (Sage) [gaussian_binomial(n,9,-4) for n in range(9,17)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=9; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 2012

%Y Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015375, A015377,A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - _Vincenzo Librandi_, Nov 04 2012

%K sign,easy

%O 9,2

%A _Olivier Gérard_