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

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

Offset

12,2

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

Formula

a(n) = Product_{i=1..12} ((-5)^(n-i+1)-1)/((-5)^i-1). - 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 *)

Prog

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

Crossrefs

Sequence in context: A317287 A132205 A358019 * A078249 A243363 A273094

Adjacent sequences: A015424 A015425 A015426 * A015428 A015429 A015430

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

More terms from Harvey P. Dale, Mar 28 2012

Status

approved