A015345 Gaussian binomial coefficient [ n,7 ] for q = -6.

1, -239945, 69088371619, -19251196169490725, 5393264335151280477835, -1509574711680960125598763925, 422593364163884169440003098013995, -118298673397216914972187267242547690325, 33116077152651051199781730118147946460139435

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..190
• Index entries for linear recurrences with constant coefficients, signature (-239945,11514768594,89124308917560,-115609163009731776,-24949102541146076160,902345215627683201024,5263661621405464657920,-6140942214464815497216)

Programs

Magma

r:=7; q:=-6; [&*[(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, -6], {n, 7, 20}] (* Vincenzo Librandi, Nov 02 2012 *)

Sage

[gaussian_binomial(n,7,-6) for n in range(7,15)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^7 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1) ). - R. J. Mathar, Sep 02 2016