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

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

Offset: 11

Author

Olivier Gérard

Keywords

• sign
• 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 = 11..200
• Index entries related to Gaussian binomial coefficients.

Crossrefs

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

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,11,-2) for n in range(11,21)] # Zerinvary Lajos, May 28 2009

Formula

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