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

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

Offset: 5

Author

Olivier Gérard, Dec 11 1999

Keywords

• sign
• easy

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)

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,5,-5) for n in range(5,15)] # Zerinvary Lajos, May 27 2009

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