A015326 Gaussian binomial coefficient [ n,6 ] for q = -4.

1, 3277, 14317213, 57741320029, 237435704507485, 971588061067577437, 3980596286193864759389, 16303527542855381993658461, 66780267552779682073190144093, 273530932713230996784935699290205

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 (3277, 3578484, -902879040, -57784258560, 938078109696, 3518651957248, -4398046511104).

Programs

Mathematica

Table[QBinomial[n, 6, -4], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-4) for n in range(6,16)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^6 / ( (x-1)*(4096*x-1)*(256*x-1)*(64*x+1)*(4*x+1)*(16*x-1)*(1024*x+1) ). - R. J. Mathar, Aug 04 2016