A015300 Gaussian binomial coefficient [ n,4 ] for q = -11.

1, 13421, 198134223, 2898705467483, 42442845454886086, 621401842151984058606, 9097949506151746630368210, 133203071884610819994409432410, 1950226184559914695131839252162415

Offset: 4

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• 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 = 4..200
• Index entries for linear recurrences with constant coefficients, signature (13421,18010982,-2179328822,-23776120181,25937424601).

Programs

Mathematica

Table[QBinomial[n, 4, -11], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-11) for n in range(4,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^4 / ( (x-1)*(11*x+1)*(121*x-1)*(1331*x+1)*(14641*x-1) ). - R. J. Mathar, Aug 03 2016