A015330 Gaussian binomial coefficient [ n,6 ] for q = -7.

1, 102943, 12363454300, 1450319733570100, 170699761008128301202, 20081461365765141084602686, 2362583929682268848603506007900, 277955299234477922983349122651265300

Offset: 6

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 = 6..200
• Index entries for linear recurrences with constant coefficients, signature (102943, 1766193051, -4228553683893, -1450393913575299, 71272260266184957,488728224518062249, -558545864083284007).

Programs

Mathematica

Table[QBinomial[n, 6, -7], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-7) for n in range(6,14)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^6 / ( (x-1)*(117649*x-1)*(16807*x+1)*(49*x-1)*(343*x+1)*(7*x+1)*(2401*x-1) ). - R. J. Mathar, Sep 02 2016