A015421 Gaussian binomial coefficient [ n,11 ] for q=-12.

1, -685853880635, 513158776998704708174485, -381060745537275503024171826161834795, 283144978428780810444903027180667803787005364693, -210378243627879792478862753186483140572522717247026752860715

Offset

11,2

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 = 11..90

Formula

a(n) = Product_{i=1..11} ((-12)^(n-i+1)-1)/((-12)^i-1)). - Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 11, -12], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -12) for n in range(11, 16)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; 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: A297006 A230559 A105302 * A335336 A180612 A092382

Adjacent sequences: A015418 A015419 A015420 * A015422 A015423 A015424

Keyword

sign,easy

Author

Olivier Gérard

Status

approved