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A015429 Gaussian binomial coefficient [ n,12 ] for q=-6. 3

%I

%S 1,1865813431,4177511710786827427,9051628015237517688012698587,

%T 19718638974813744289323111717093729163,

%U 42917665763197914342331213431251480044434903403

%N Gaussian binomial coefficient [ n,12 ] for q=-6.

%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="/A015429/b015429.txt">Table of n, a(n) for n = 12..120</a>

%F a(n) = Product_{i=1..12} ((-6)^(n-i+1)-1)/((-6)^i-1). - _Vincenzo Librandi_, Nov 06 2012

%t Table[QBinomial[n, 12, -6], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)

%o (Sage) [gaussian_binomial(n,12,-6) for n in range(12,18)] # _Zerinvary Lajos_, May 28 2009

%o (MAGMA) r:=12; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012

%K nonn,easy

%O 12,2

%A _Olivier GĂ©rard_

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)