A015429 Gaussian binomial coefficient [ n,12 ] for q=-6.

1, 1865813431, 4177511710786827427, 9051628015237517688012698587, 19718638974813744289323111717093729163, 42917665763197914342331213431251480044434903403

Offset: 12

Author

Olivier Gérard

Keywords

• nonn
• 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 = 12..120

Programs

Magma

r:=12; q:=-6; [&*[(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, 12, -6], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,12,-6) for n in range(12,18)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..12} ((-6)^(n-i+1)-1)/((-6)^i-1). - Vincenzo Librandi, Nov 06 2012