A015327 Gaussian binomial coefficient [ n,6 ] for q = -5.

1, 13021, 211929796, 3285123767796, 51412313316921546, 803060432690378496546, 12548622321219854387027796, 196069714237340352552410777796, 3063597127265150338968694860387171

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 (13021, 42383355, -26287771375, -3285971421875, 82779990234375, 397369384765625, -476837158203125).

Programs

Mathematica

Table[QBinomial[n, 6, -5], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-5) for n in range(6,15)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^6 /((x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(125*x+1)*(15625*x-1)*(3125*x+1)). - R. J. Mathar, Sep 02 2016