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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 xrange(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 March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)