A015424 Gaussian binomial coefficient [ n,12 ] for q=-3.

1, 398581, 238300021051, 122119467087816511, 65710531328480659504924, 34778150788062009177434607244, 18507923283033747485964552371646724, 9831373896055842251635498188040677794164

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..180

Programs

Magma

r:=12; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 06 2012

Mathematica

QBinomial[Range[12,20],12,-3] (* Harvey P. Dale, Dec 18 2011 *)
Table[QBinomial[n, 12, -3], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,12,-3) for n in range(12,20)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..12} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012