A015277 Gaussian binomial coefficient [ n,3 ] for q = -9.

1, -656, 484210, -352504880, 257015284435, -187360965026144, 136586400868021924, -99571465386311288480, 72587599955185580267365, -52916360230556551635386480, 38576026619154398792076180886

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 range(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 A309963 A289290

Adjacent sequences: A015274 A015275 A015276 * A015278 A015279 A015280

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved