A015328 Gaussian binomial coefficient [ n,6 ] for q = -6.

1, 39991, 1919128099, 89126228045659, 4161484248724884235, 194133243948726244454635, 9057674762915720387519905195, 422593364163884169440003098013995

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 (39991, 319848018, -412665849288, -89135823446208, 3223331091606528, 18803167718178816, -21936950640377856).

Programs

Mathematica

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

Sage

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

Formula

G.f.: x^6 /((x-1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1)). - R. J. Mathar, Sep 02 2016