A015309 Gaussian binomial coefficient [ n,5 ] for q = -5.

1, -2604, 8476671, -26279294704, 82254445109046, -256962886520659704, 803060432690378496546, -2509531719872244898534704, 7842306707330337276457324671, -24507195908707737696414306347204

Offset

5,2

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 = 5..200

Index entries for linear recurrences with constant coefficients, signature (-2604,1695855,209963000,-5299546875,-25429687500,30517578125)

Formula

G.f.: -x^5 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(125*x+1)*(3125*x+1) ). - R. J. Mathar, Aug 04 2016

Mathematica

Table[QBinomial[n, 5, -5], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Prog

(Sage) [gaussian_binomial(n, 5, -5) for n in range(5, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=5; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Aug 03 2016

Crossrefs

Sequence in context: A031729 A001726 A109487 * A212083 A236889 A254695

Adjacent sequences: A015306 A015307 A015308 * A015310 A015311 A015312

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved