A015344 Gaussian binomial coefficient [ n,7 ] for q = -5.

1, -65104, 5298179796, -410635172794704, 32132285187903171546, -2509531719872244898534704, 196069714237340352552410777796, -15317750355077977702804539604534704, 1196702310087594273181943625299134137171

Offset

7,2

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 = 7..200

Index entries for linear recurrences with constant coefficients, signature (-65104,1059648980,3284911838000,-2057018110093750,-256633737343750000,6467584106445312500,31044006347656250000,-37252902984619140625).

Formula

G.f.: x^7 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(78125*x+1)*(125*x+1)*(15625*x-1)*(3125*x+1) ). - R. J. Mathar, Sep 02 2016

Mathematica

Table[QBinomial[n, 7, -5], {n, 7, 20}] (* Vincenzo Librandi, Nov 02 2012 *)

Prog

(SageMath) [gaussian_binomial(n, 7, -5) for n in range(7, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=7; q:=-5; [&*[(1 - q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012

Crossrefs

Sequence in context: A183975 A234908 A204640 * A184148 A083608 A102277

Adjacent sequences: A015341 A015342 A015343 * A015345 A015346 A015347

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved