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Gaussian binomial coefficient [ n,4 ] for q = -7.
2

%I #25 Sep 08 2022 08:44:39

%S 1,2101,5149551,12328144851,29612203932102,71094673339606302,

%T 170699761008128301202,409849628721453245181802,

%U 984049129188697468764456303,2362701900656492615160524472603,5672847283550509352791825564114953,13620506320919298149305087013514770853

%N Gaussian binomial coefficient [ n,4 ] for q = -7.

%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="/A015293/b015293.txt">Table of n, a(n) for n = 4..300</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2101, 735350, -36032150, -247180549, 282475249).

%t QBinomial[Range[4,17],4,-7] (* _Harvey P. Dale_, Sep 24 2011 *)

%t Table[QBinomial[n, 4, -7], {n, 4, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)

%o (Sage) [gaussian_binomial(n,4,-7) for n in range(4,14)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=4; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016

%K nonn,easy

%O 4,2

%A _Olivier GĂ©rard_, Dec 11 1999

%E More terms from _Harvey P. Dale_, Sep 24 2011