A015349 Gaussian binomial coefficient [ n,7 ] for q = -9.

1, -4304672, 20846476694116, -99571465386311288480, 476319830905927777714449130, -2278184404047301621409794099651808, 10896505884544222754038383150470776581556, -52117638957586712017437457380440909324731738208

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..150

Programs

Magma

r:=7; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012

Mathematica

QBinomial[Range[7,20],7,-9] (* Harvey P. Dale, Dec 28 2011 *)

Sage

[gaussian_binomial(n,7,-9) for n in range(7,14)] # Zerinvary Lajos, May 27 2009

Extensions

One more term from Harvey P. Dale, Dec 28 2011