A015436 Gaussian binomial coefficient [ n,12 ] for q=-12.

1, 8230246567621, 73894863887821708223693461, 658472968288485964089656737315874219221, 5871294272699857358353797657582417236064659116493269, 52348839118418455816373076458257326632599555195248225626953928149

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..90

Formula

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

Mathematica

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

Prog

(SageMath) [gaussian_binomial(n, 12, -12) for n in range(12, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; q:=-12; [&*[(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: A186179 A058124 A282540 * A183078 A057074 A017412

Adjacent sequences: A015433 A015434 A015435 * A015437 A015438 A015439

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved