%I #31 Sep 08 2022 08:44:39
%S 1,21,546,13546,339171,8476671,211929796,5298179796,132454820421,
%T 3311368882921,82784230211046,2069605714586046,51740143068101671,
%U 1293503575685289171,32337589397218492296,808439734905030992296
%N Gaussian binomial coefficient [ n,2 ] for q = -5.
%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="/A015255/b015255.txt">Table of n, a(n) for n = 2..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,105,-125).
%F G.f.: x^2/((1-x)*(1+5*x)*(1-25*x)).
%F a(0)=1, a(1)=21, a(2)=546, a(n) = 21*a(n-1) + 105*a(n-2) - 125*a(n-3). - _Harvey P. Dale_, Jun 24 2011
%t Table[QBinomial[n,2,-5],{n,2,22}] (* or *) LinearRecurrence[ {21,105,-125}, {1,21,546},21] (* _Harvey P. Dale_, Jun 24 2011 *)
%o (Sage) [gaussian_binomial(n,2,-5) for n in range(2,18)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) I:=[1, 21, 546]; [n le 3 select I[n] else 21*Self(n-1) + 105*Self(n-2) - 125*Self(n-3): n in [1..30]] // _Vincenzo Librandi_, Oct 27 2012
%K nonn,easy
%O 2,2
%A _Olivier GĂ©rard_, Dec 11 1999