A015338 Gaussian binomial coefficient [ n,7 ] for q = -2.

1, -85, 14535, -1652145, 225683007, -28005209505, 3642010817055, -462535373765985, 59438516325245343, -7593183562134412385, 972884994173649887135, -124468028808034701006945

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

• G. C. Greubel, Table of n, a(n) for n = 7..450[Terms 7 through 200 were computed by Vincenzo Librandi; terms 201 to 450 by G. C. Greubel, Nov 06 2016]

Crossrefs

Diagonal k=7 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Programs

Magma

/* By definition: */ r:=7; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Bruno Berselli, Oct 30 2012

Mathematica

Table[QBinomial[n, 7, -2], {n, 7, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,7,-2) for n in range(7,19)] # Zerinvary Lajos, May 27 2009