A015279 Gaussian binomial coefficient [ n,3 ] for q = -11.

1, -1220, 1637362, -2177691460, 2898705467483, -3858153003126520, 5135204548028317764, -6834956902420811530200, 9097327679593690752247605, -12108543136400139930131294300, 16116470915170412804822871108406

Offset: 3

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 = 3..200
• Index entries for linear recurrences with constant coefficients, signature (-1220,148962,1623820,-1771561).

Programs

Magma

r:=3; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

Mathematica

Table[QBinomial[n, 3, -11], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,3,-11) for n in range(3,14)] # Zerinvary Lajos, May 27 2009

Formula

a(n) = product(((-11)^(n-i+1)-1)/((-11)^i-1), i=1..3) (by definition). - Vincenzo Librandi, Aug 02 2016

G.f.: x^3 / ( (x-1)*(11*x+1)*(121*x-1)*(1331*x+1) ). - R. J. Mathar, Aug 03 2016