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%I #24 Sep 08 2022 08:44:39
%S 1,111,13542,1637362,198134223,23974093353,2900866919644,
%T 351004879413684,42471590605551405,5139062461110267955,
%U 621826557818118395106,75241013495730790109766,9104162632986302495960347,1101603678591310956191736717
%N Gaussian binomial coefficient [ n,2 ] for q = -11.
%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="/A015262/b015262.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 (111, 1221, -1331).
%F G.f.: x^2/((1-x)*(1+11*x)*(1-121*x)).
%F a(2) = 1, a(3) = 111, a(4) = 13542, a(n) = 111*a(n-1) + 1221*a(n-2) - 1331*a(n-3). - _Vincenzo Librandi_, Oct 28 2012
%t Table[QBinomial[n, 2, -11], {n, 2, 20}] (* _Vincenzo Librandi_, Oct 28 2012 *)
%o (Sage) [gaussian_binomial(n,2,-11) for n in range(2,14)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) I:=[1, 111, 13542]; [n le 3 select I[n] else 111*Self(n-1) + 1221*Self(n-2) - 1331*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 28 2012
%K nonn,easy
%O 2,2
%A _Olivier Gérard_, Dec 11 1999
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