A015275 Gaussian binomial coefficient [ n,3 ] for q = -7.

1, -300, 105050, -35927100, 12328144851, -4228301370600, 1450319733570100, -497459062806004200, 170628488227082949701, -58525570007342935110900, 20074270583791406305395150, -6885474806748086165925231300

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 (-300,15050,102900,-117649).

Formula

G.f.: x^3/((1-x)*(1+7*x)*(1-49*x)*(1+343*x)). - Bruno Berselli, Oct 30 2012

a(n) = (-1 + 43*7^(2n-3) + (-1)^n*7^(n-2)*(43-7^(2n-1)))/132096. - Bruno Berselli, Oct 30 2012

Mathematica

QBinomial[Range[3, 20], 3, -7] (* Harvey P. Dale, Apr 09 2012 *)
Table[QBinomial[n, 3, -7], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 3, -7) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=-7; [&*[(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: A190880 A063935 A294687 * A051306 A151609 A004225

Adjacent sequences: A015272 A015273 A015274 * A015276 A015277 A015278

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved