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

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

Offset: 7

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 = 7..200
• Index entries for linear recurrences with constant coefficients, signature (-65104,1059648980,3284911838000,-2057018110093750,-256633737343750000,6467584106445312500,31044006347656250000,-37252902984619140625).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,7,-5) for n in range(7,15)] # Zerinvary Lajos, May 27 2009

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