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 A015424 Gaussian binomial coefficient [ n,12 ] for q=-3. 2

%I

%S 1,398581,238300021051,122119467087816511,65710531328480659504924,

%T 34778150788062009177434607244,18507923283033747485964552371646724,

%U 9831373896055842251635498188040677794164

%N Gaussian binomial coefficient [ n,12 ] for q=-3.

%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="/A015424/b015424.txt">Table of n, a(n) for n = 12..180</a>

%F a(n) = Product_{i=1..12} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - _Vincenzo Librandi_, Nov 06 2012

%t QBinomial[Range[12,20],12,-3] (* _Harvey P. Dale_, Dec 18 2011 *)

%t Table[QBinomial[n, 12, -3], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)

%o (Sage) [gaussian_binomial(n,12,-3) for n in range(12,20)] # _Zerinvary Lajos_, May 28 2009

%o (MAGMA) r:=12; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 06 2012

%K nonn,easy

%O 12,2