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%I #31 Sep 08 2022 08:44:39
%S 1,11,231,3311,56287,875007,14208447,225683007,3624203583,57881286463,
%T 926949282623,14824402656063,237244744338239,3795481554332479,
%U 60731179948567359,971671079497526079,15546959673214593855
%N Gaussian binomial coefficient [ n,4 ] 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="/A015287/b015287.txt">Table of n, a(n) for n = 4..800</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,110,-440,-704,1024).
%H <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.
%F G.f.: x^4/((1-x)*(1+2*x)*(1-4*x)*(1+8*x)*(1-16*x)). - _Bruno Berselli_, Oct 30 2012
%F a(n) = (1 - 2^(2n-5)*(15-2^(2n-1)) - (-1)^n*5*2^(n-3)*(1-2^(2n-3)))/1215. - _Bruno Berselli_, Oct 30 2012
%F A015287(n) = T[n,4], where T is the triangular array A015109. - _M. F. Hasler_, Nov 04 2012
%t Table[QBinomial[n, 4, -2], {n, 4, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o (Sage) [gaussian_binomial(n,4,-2) for n in range(4,21)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=4; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016
%Y Diagonal k=4 in the triangular array A015109. See there for further references and programs. - _M. F. Hasler_, Nov 04 2012
%K nonn,easy
%O 4,2
%A _Olivier Gérard_, Dec 11 1999
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