A015405 Gaussian binomial coefficient [ n,11 ] for q=-2.

1, -1365, 3727815, -6785865905, 14824402656063, -29439916001972385, 61250446192484546335, -124468028808034701006945, 255910660218571393553843871, -523082886040328458081329117025

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..200

Index entries related to Gaussian binomial coefficients.

Formula

a(n) = Product_{i=1..11} ((-2)^(n-i+1)-1)/((-2)^i-1). - Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 11, -2], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Prog

(Sage) [gaussian_binomial(n, 11, -2) for n in range(11, 21)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 05 2012

Crossrefs

Diagonal k=11 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Sequence in context: A096117 A140936 A022204 * A295466 A292780 A180089

Adjacent sequences: A015402 A015403 A015404 * A015406 A015407 A015408

Keyword

sign,easy

Author

Olivier Gérard

Status

approved