A015319 Gaussian binomial coefficient [ n,5 ] for q = -12.

1, -229691, 57554154133, -14313032243145515, 3561712204486990461397, -886264409554702323499876907, 220531019414004693731359534452181, -54875173091354091477849994502919434795

Offset: 5

Author

Olivier Gérard, Dec 11 1999

Keywords

• sign
• 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 = 5..190
• Index entries for linear recurrences with constant coefficients, signature (-229691,4796198652,8282638393920,-1193447702974464,-14221861305974784,15407021574586368).

Programs

Mathematica

Table[QBinomial[n, 5, -12], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,5,-12) for n in range(5,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^5 / ( (x-1)*(1728*x+1)*(20736*x-1)*(12*x+1)*(248832*x+1)*(144*x-1) ). - R. J. Mathar, Aug 04 2016