A015332 Gaussian binomial coefficient [ n,6 ] for q = -9.

1, 478297, 257363962948, 136586400868021924, 72598678627860564552010, 38581260992855637306941215162, 20503702504565185601675453268123604, 10896505884544222754038383150470776581556

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..180

Programs

Mathematica

Table[QBinomial[n, 6, -9], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-9) for n in range(6,14)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^6/((1-x)*(1+9*x)*(1-81*x)*(1+729*x)*(1-6561*x)*(1+59049*x)*(1-531441*x)). - Vincenzo Librandi, Oct 30 2012