A015317 Gaussian binomial coefficient [ n,5 ] for q = -11.

1, -147630, 23974093353, -3858153003126520, 621401842151984058606, -100076766678577032638496300, 16117472448301015835209097979510, -2595734922068255016665440444288632600

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..200

Programs

Mathematica

Table[QBinomial[n, 5, -11], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,5,-11) for n in range(5,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^5/((1 - x)*(1 + 11*x)*(1 - 121*x)*(1 + 1331*x)*(1 - 14641*x)*(1 + 161051*x)). - Ilya Gutkovskiy, Aug 16 2016