login
Gaussian binomial coefficient [ n,7 ] for q = -3.
2

%I #19 Dec 07 2019 12:18:18

%S 1,-1640,4035220,-8509702520,18843459775162,-41041673208656120,

%T 89881489830655851460,-196480936769813691291560,

%U 429769342296322230713871283,-939857780045414554730512966640

%N Gaussian binomial coefficient [ n,7 ] for q = -3.

%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="/A015340/b015340.txt">Table of n, a(n) for n = 7..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1640,1345620,314875080,-25929962838,-688631799960,6436058745780,17154979252920,-22876792454961).

%F G.f.: x^7 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(2187*x+1)*(3*x+1)*(243*x+1) ). - _R. J. Mathar_, Sep 02 2016

%t Table[QBinomial[n, 7, -3], {n, 7, 20}] (* _Vincenzo Librandi_, Oct 29 2012 *)

%o (Sage) [gaussian_binomial(n,7,-3) for n in range(7,17)] # _Zerinvary Lajos_, May 27 2009

%K sign,easy

%O 7,2

%A _Olivier GĂ©rard_, Dec 11 1999