A015324 Gaussian binomial coefficient [ n,6 ] for q = -3.

1, 547, 448540, 315323620, 232740363922, 168973319623174, 123350523324917020, 89881489830655851460, 65533580739687859229563, 47771556642163840723529281, 34826053765400471578213696840

Offset

6,2

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 = 6..200

Index entries for linear recurrences with constant coefficients, signature (547,149331,-11711817,-316219059,2939282073,7848852129,-10460353203).

Formula

G.f.: x^6 / ( (x-1)*(27*x+1)*(81*x-1)*(729*x-1)*(9*x-1)*(3*x+1)*(243*x+1) ). - R. J. Mathar, Aug 04 2016

Mathematica

Table[QBinomial[n, 6, -3], {n, 6, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

Prog

(Sage) [gaussian_binomial(n, 6, -3) for n in range(6, 17)] # Zerinvary Lajos, May 27 2009

Crossrefs

Sequence in context: A263524 A300899 A253546 * A103537 A136928 A249297

Adjacent sequences: A015321 A015322 A015323 * A015325 A015326 A015327

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved