A015341 Gaussian binomial coefficient [ n,7 ] for q = -4.

1, -13107, 229062301, -3695215419555, 60779845138496605, -994845394688060798883, 16303527542855381993658461, -267100691734599723202106566563, 4376244513647234644625387176712285

Offset: 7

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 = 7..200
• Index entries for linear recurrences with constant coefficients, signature (-13107,57268852,57727002816,-14850554449920,-945799214137344,15372990401216512,57645195621040128,-72057594037927936).

Programs

Mathematica

Table[QBinomial[n, 7, -4], {n, 7, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,7,-4) for n in range(7,16)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^7 / ( (x-1)*(16384*x+1)*(4096*x-1)*(256*x-1)*(64*x+1)*(4*x+1)*(16*x-1)*(1024*x+1) ). - R. J. Mathar, Sep 02 2016