A015291 Gaussian binomial coefficient [ n,4 ] for q = -5.

1, 521, 339171, 210302171, 131649159046, 82254445109046, 51412313316921546, 32132285187903171546, 20082729571968536374671, 12551699566292514833249671, 7844813030956382105126218421

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..300
• Index entries for linear recurrences with constant coefficients, signature (521,67730,-1693250,-8140625,9765625).

Programs

Magma

r:=4; q:=-5; [&*[(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, -5], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-5) for n in range(4,15)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^4 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(125*x+1) ). - R. J. Mathar, Aug 03 2016