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

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

Offset: 5

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 = 5..100
• Index entries for linear recurrences with constant coefficients, signature (-14706,36046857,12322995300,-605839525599,-4154081011794,4747561509943).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,5,-7) for n in range(5,14)] # Zerinvary Lajos, May 27 2009

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