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

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

Offset

5,2

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)

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A131645 A186086 A236733 * A043516 A046410 A326811

Adjacent sequences: A015307 A015308 A015309 * A015311 A015312 A015313

Keyword

sign,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved