%I #18 Sep 08 2022 08:44:39
%S 1,-28242953648,897372484611991440598,
%T -28121923404466184234811544425296,
%U 882630281467161063728449241801432249226565,-27697404417453539188846019907159858548132165589760832,869175534545800426775448129124238227336771807766117241522242296
%N Gaussian binomial coefficient [ n,11 ] 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="/A015414/b015414.txt">Table of n, a(n) for n = 11..100</a>
%F a(n) = Product_{i=1..11} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - _Vincenzo Librandi_, Nov 06 2012
%t Table[QBinomial[n, 11, -9], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)
%o (Sage) [gaussian_binomial(n,11,-9) for n in range(11,17)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=11; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012
%K sign,easy
%O 11,2
%A _Olivier GĂ©rard_
|