A015289 Gaussian binomial coefficient [ n,4 ] for q = -4.

1, 205, 55965, 14107485, 3625623645, 927257668701, 237435704507485, 60779845138496605, 15559876852907031645, 3983313338565919030365, 1019729183363623510391901, 261050608944894743386831965

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..400
• Index entries for linear recurrences with constant coefficients, signature (205,13940,-223040,-839680,1048576).

Programs

Magma

r:=4; q:=-4; [&*[(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, -4], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-4) for n in range(4,16)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^4 / ( (x-1)*(256*x-1)*(64*x+1)*(4*x+1)*(16*x-1) ). - R. J. Mathar, Aug 03 2016