A015315 Gaussian binomial coefficient [ n,5 ] for q = -9.

1, -53144, 3177326971, -187360965026144, 11065164158125239526, -653375813208979143531248, 38581260992855637306941215162, -2278184404047301621409794099651808

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 (-53144,353042235,256976057520,-20846790934515,-185301670206744,205891132094649).

Programs

Mathematica

Table[QBinomial[n, 5, -9], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,5,-9) for n in range(5,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^5 / ( (x-1)*(81*x-1)*(9*x+1)*(729*x+1)*(6561*x-1)*(59049*x+1) ). - R. J. Mathar, Aug 04 2016