A015427 Gaussian binomial coefficient [ n,12 ] for q=-5.

1, 203450521, 51740143068101671, 12531617923263572089314671, 3064380040090865325461356053952796, 747900330120650910670378436164144443652796, 182604540723920504029015495725080327984747417027796, 44580616068292567497216163076570130750072904955316534527796

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..130

Programs

Magma

r:=12; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Mathematica

QBinomial[Range[12,20],12,-5] (* Harvey P. Dale, Mar 28 2012 *)
Table[QBinomial[n, 12, -5], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,12,-5) for n in range(12,18)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..12} ((-5)^(n-i+1)-1)/((-5)^i-1). - Vincenzo Librandi, Nov 06 2012

Extensions

More terms from Harvey P. Dale, Mar 28 2012