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 A015277 Gaussian binomial coefficient [ n,3 ] for q = -9. 2
 1, -656, 484210, -352504880, 257015284435, -187360965026144, 136586400868021924, -99571465386311288480, 72587599955185580267365, -52916360230556551635386480, 38576026619154398792076180886 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 REFERENCES 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. I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99. M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. LINKS Vincenzo Librandi, Table of n, a(n) for n = 3..200 Index entries for linear recurrences with constant coefficients, signature (-656,53874,478224,-531441). FORMULA G.f.: x^3/((1-x)*(1+9*x)*(1-81*x)*(1+729*x)). - Bruno Berselli, Oct 30 2012 a(n) = (-1 + 73*3^(4n-6) + (-1)^n*3^(2n-4)*(73-3^(4n-2)))/584000. - Bruno Berselli, Oct 30 2012 a(n) = product(((-9)^(n-i+1)-1)/((-9)^i-1), i=1..3) (by definition). - Vincenzo Librandi, Aug 02 2016 MATHEMATICA Table[QBinomial[n, 3, -9], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *) LinearRecurrence[{-656, 53874, 478224, -531441}, {1, -656, 484210, -352504880}, 20] (* Harvey P. Dale, Feb 10 2015 *) PROG (Sage) [gaussian_binomial(n, 3, -9) for n in xrange(3, 14)] # Zerinvary Lajos, May 27 2009 (MAGMA) r:=3; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016 CROSSREFS Sequence in context: A252680 A233898 A088894 * A135418 A289290 A034818 Adjacent sequences:  A015274 A015275 A015276 * A015278 A015279 A015280 KEYWORD sign,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

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Last modified March 26 20:36 EDT 2019. Contains 321534 sequences. (Running on oeis4.)