A015421 Gaussian binomial coefficient [ n,11 ] for q=-12.

1, -685853880635, 513158776998704708174485, -381060745537275503024171826161834795, 283144978428780810444903027180667803787005364693, -210378243627879792478862753186483140572522717247026752860715

Offset: 11

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 = 11..90

Programs

Magma

r:=11; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 11, -12], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,11,-12) for n in range(11,16)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..11} ((-12)^(n-i+1)-1)/((-12)^i-1). - Vincenzo Librandi, Nov 06 2012