A015346 Gaussian binomial coefficient [ n,7 ] for q = -7.

1, -720600, 605808540100, -497459062806004200, 409849628721453245181802, -337508711324786004755672161800, 277955299234477922983349122651265300, -228907863042160417649553303166468327692600

Offset: 7

Author

Olivier Gérard, Dec 11 1999

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 = 7..170

Programs

Magma

r:=7; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012

Mathematica

Table[QBinomial[n, 7, -7], {n, 7, 20}] (* Vincenzo Librandi, Nov 02 2012 *)

Sage

[gaussian_binomial(n,7,-7) for n in range(7,15)] # Zerinvary Lajos, May 27 2009