A015354 Gaussian binomial coefficient [ n,7 ] for q = -12.

1, -33075515, 1193443303932565, -42738498397393357626155, 1531471524472711661173885667797, -54875173091354091477849994502919434795, 1966277324678482270775562667263264108238642645, -70455269606355713779351701809782497716434153197609515

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..140

Programs

Magma

r:=7; q:=-12; [&*[(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,-12] (* Harvey P. Dale, Mar 17 2012 *)

Sage

[gaussian_binomial(n,7,-12) for n in range(7,13)] # Zerinvary Lajos, May 27 2009

Extensions

More terms from Harvey P. Dale, Mar 17 2012