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A015432 Gaussian binomial coefficient [ n,12 ] for q=-9. 2

%I

%S 1,254186582833,72687171253825493271271,

%T 20500882161928535478431441379312055,

%U 5790937276726544621284284010937628428554805020,1635504033452004972838895174119166771419593874338342173788,461915515256190228639422934162753182948200513062452706826160310202324

%N Gaussian binomial coefficient [ n,12 ] 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="/A015432/b015432.txt">Table of n, a(n) for n = 12..100</a>

%F a(n) = Product_{i=1..12} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - _Vincenzo Librandi_, Nov 06 2012

%t Table[QBinomial[n, 12, -9], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)

%o (Sage) [gaussian_binomial(n,12,-9) for n in xrange(12,17)] # _Zerinvary Lajos_, May 28 2009

%o (MAGMA) r:=12; q:=-9; [&*[(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 April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)