A015376 Gaussian binomial coefficient [ n,9 ] for q=-4.

1, -209715, 58640578205, -15135778281070755, 3983313338565919030365, -1043182954580986851130914723, 273530932713230996784935699290205, -71700116580663579186545558567554787235, 18796042166858164201094703719132482337953885

Offset: 9

Author

Olivier Gérard

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 = 9..190

Crossrefs

Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015375, A015377,A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Programs

Magma

r:=9; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 9, -4],{n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Sage

[gaussian_binomial(n,9,-4) for n in range(9,17)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..9} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

G.f.: -x^9 / ( (x-1)*(16384*x+1)*(4096*x-1)*(256*x-1)*(65536*x-1)*(64*x+1)*(262144*x+1)*(4*x+1)*(16*x-1)*(1024*x+1) ). - R. J. Mathar, Sep 02 2016