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

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

Offset: 4

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• 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 = 4..500
• Index entries related to Gaussian binomial coefficients.
• Index entries for linear recurrences with constant coefficients, signature (61,1830,-16470,-44469,59049).

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,4,-3) for n in range(4,17)] # Zerinvary Lajos, May 27 2009

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