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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
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.
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
(SageMath) [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
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved