A015288 Gaussian binomial coefficient [ n,4 ] for q = -3.

1, 61, 5551, 433771, 35569222, 2869444942, 232740363922, 18843459775162, 1526550040078063, 123644349019377043, 10015359787639069513, 811239619864365082573, 65710531328480659504924

Offset

4,2

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 = 4..500

Index entries related to Gaussian binomial coefficients.

Index entries for linear recurrences with constant coefficients, signature (61,1830,-16470,-44469,59049).

Formula

G.f.: -x^4 / ( (x-1)*(27*x+1)*(81*x-1)*(9*x-1)*(3*x+1) ). - R. J. Mathar, Aug 03 2016

Mathematica

Table[QBinomial[n, 4, -3], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

(Sage) [gaussian_binomial(n, 4, -3) for n in range(4, 17)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

Crossrefs

Sequence in context: A165259 A181636 A167736 * A219113 A210686 A103915

Adjacent sequences: A015285 A015286 A015287 * A015289 A015290 A015291

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved