A015310 Gaussian binomial coefficient [ n,5 ] for q = -6.

1, -6665, 53308003, -412612541285, 3210953026617931, -24965159781954413525, 194133243948726244454635, -1509574711680960125598763925, 11738459947705882553575280369515, -91278255494743382265330154281509525

Offset: 5

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 = 5..200
• Index entries for linear recurrences with constant coefficients, signature (-6665,8885778,1909009080,-69095809728,-403007063040,470184984576)

Programs

Magma

r:=5; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Aug 03 2016

Mathematica

Table[QBinomial[n, 5, -6], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,5,-6) for n in range(5,15)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^5 / ( (x-1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1) ). - R. J. Mathar, Aug 04 2016