A015313 Gaussian binomial coefficient [ n,5 ] for q = -8.

1, -29127, 969583737, -31709385606535, 1039306892330748537, -34054968941001637311879, 1115917479276007905665796729, -36566366524181816928510601278855

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
• Index entries for linear recurrences with constant coefficients, signature (-29127,121201608,61919137280,-3971534290944,-31274878107648,35184372088832).

Programs

Mathematica

Table[QBinomial[n, 5, -8], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,5,-8) for n in range(5,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^5 / ( (x-1)*(8*x+1)*(64*x-1)*(512*x+1)*(32768*x+1)*(4096*x-1) ). - R. J. Mathar, Aug 04 2016