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 A015268 Gaussian binomial coefficient [ n,3 ] for q = -3. 2
 1, -20, 610, -15860, 433771, -11662040, 315323620, -8509702520, 229798289941, -6204226946060, 167517069529030, -4522934399547980, 122119467087816511, -3297223466672052080, 89025052902439936840, -2403676254645238280240 (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 (-20,210,540,-729). FORMULA G.f.: x^3/((1-x)*(1+3*x)*(1-9*x)*(1+27*x)). - Bruno Berselli, Oct 29 2012 a(n) = (-1 + 7*3^(2n-3) + (-1)^n*3^(n-2)*(7-3^(2n-1)))/896. - Bruno Berselli, Oct 29 2012 MATHEMATICA Table[QBinomial[n, 3, -3], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *) PROG (Sage) [gaussian_binomial(n, 3, -3) for n in range(3, 19)] # Zerinvary Lajos, May 27 2009 (MAGMA) [(-1+7*3^(2*n-3)+(-1)^n*3^(n-2)*(7-3^(2*n-1)))/896: n in [3..18]]; // Bruno Berselli, Oct 29 2012 (Maxima) makelist(coeff(taylor(1/((1-x)*(1+3*x)*(1-9*x)*(1+27*x)), x, 0, n), x, n), n, 0, 15); \\ Bruno Berselli, Oct 29 2012 CROSSREFS Sequence in context: A027407 A116218 A035279 * A202577 A059420 A129906 Adjacent sequences:  A015265 A015266 A015267 * A015269 A015270 A015271 KEYWORD sign,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

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Last modified May 8 08:51 EDT 2021. Contains 343666 sequences. (Running on oeis4.)