A015312 Gaussian binomial coefficient [ n,5 ] for q = -7.

1, -14706, 252313293, -4228301370600, 71094673339606302, -1194817080145423511412, 20081461365765141084602686, -337508711324786004755672161800, 5672509895284807570626050787828903

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..100

Index entries for linear recurrences with constant coefficients, signature (-14706,36046857,12322995300,-605839525599,-4154081011794,4747561509943).

Formula

G.f.: -x^5 / ( (x-1)*(16807*x+1)*(49*x-1)*(343*x+1)*(7*x+1)*(2401*x-1) ). - R. J. Mathar, Aug 04 2016

Mathematica

QBinomial[Range[5, 20], 5, -7] (* Harvey P. Dale, Feb 27 2012 *)

Prog

(Sage) [gaussian_binomial(n, 5, -7) for n in range(5, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=5; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Aug 03 2016

Crossrefs

Sequence in context: A013861 A291145 A256839 * A219068 A023333 A249464

Adjacent sequences: A015309 A015310 A015311 * A015313 A015314 A015315

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved