A015298 Gaussian binomial coefficient [ n,4 ] for q = -10.

1, 9091, 91828191, 917364637191, 9174563736547191, 91744720010017447191, 917448117456547208447191, 9174480257209191175298447191, 91744803489448201844894398447191

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..200
• Index entries for linear recurrences with constant coefficients, signature (9091,9181910,-918191000,-9091000000,10000000000).

Programs

Magma

r:=4; q:=-10; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Aug 03 2016

Mathematica

Table[QBinomial[n, 4, -10], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-10) for n in range(4,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^4 / ( (x-1)*(10*x+1)*(1000*x+1)*(100*x-1)*(10000*x-1) ). - R. J. Mathar, Aug 03 2016