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%I #25 Sep 08 2022 08:44:39
%S 1,73,5986,484210,39226915,3177326971,257363962948,20846476694116,
%T 1688564650965445,136773736379522605,11078672649879436966,
%U 897372484611991440598,72687171253825493271271,5887660871557577275727455,476900530596184348447133320
%N Gaussian binomial coefficient [ n,2 ] for q = -9.
%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="/A015260/b015260.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 (73, 657, -729).
%F G.f.: x^2/((1-x)*(1+9*x)*(1-81*x)).
%F a(2) = 1, a(3) = 73, a(4) = 5986, a(n) = 73*a(n-1) + 657*a(n-2) - 729*a(n-3). - _Vincenzo Librandi_, Oct 27 2012
%t Table[QBinomial[n, 2, -9], {n, 2, 20}] (* _Vincenzo Librandi_, Oct 27 2012 *)
%o (Sage) [gaussian_binomial(n,2,-9) for n in range(2,15)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) I:=[1, 73, 5986]; [n le 3 select I[n] else 73*Self(n-1) + 657*Self(n-2) - 729*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 27 2012
%K nonn,easy
%O 2,2
%A _Olivier Gérard_, Dec 11 1999
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