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

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

Offset

5,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A212727 A234670 A324636 * A270515 A179624 A357826

Adjacent sequences: A015316 A015317 A015318 * A015320 A015321 A015322

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved