A015316 Gaussian binomial coefficient [ n,5 ] for q = -10.

1, -90909, 9182728191, -917355454462809, 91744720010017447191, -9174380256281734701652809, 917438943076290926712489347191, -91743885133148835462057759420652809

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 (-90909,918281910,917272809000,-91828191000000,-909090000000000,1000000000000000).

Programs

Mathematica

Table[QBinomial[n, 5, -10], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,5,-10) for n in range(5,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^5 / ( (x-1)*(10*x+1)*(1000*x+1)*(100*x-1)*(10000*x-1)*(100000*x+1) ). - R. J. Mathar, Aug 04 2016