A015281 Gaussian binomial coefficient [ n,3 ] for q = -12.

1, -1595, 2775445, -4793193515, 8283038077141, -14313032243145515, 24732928003956401365, -42738498397393357626155, 73852125402551558141191381, -127616472670861852065241422635

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 (-1595,231420,2756160,-2985984).

Formula

a(n) = Product_{i=1..3} ((-12)^(n-i+1)-1)/((-12)^i-1) (by definition). - Vincenzo Librandi, Aug 02 2016

G.f.: x^3 / ( (x-1)*(12*x+1)*(1728*x+1)*(144*x-1) ). - R. J. Mathar, Aug 03 2016

Mathematica

Table[QBinomial[n, 3, -12], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 3, -12) for n in range(3, 13)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=-12; [&*[(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: A316336 A028893 A029561 * A132654 A224946 A316335

Adjacent sequences: A015278 A015279 A015280 * A015282 A015283 A015284

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved