A015295 Gaussian binomial coefficient [ n,4 ] for q = -9.

1, 5905, 39226915, 257015284435, 1686534296462470, 11065164158125239526, 72598678627860564552010, 476319830905927777714449130, 3125134483161392104770081009295, 20504007291105533368839949866598015

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.
• M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
• I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..200
• Index entries for linear recurrences with constant coefficients, signature (5905,4357890,-352989090,-3138159105,3486784401)

Programs

Magma

r:=4; q:=-9; [&*[(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, -9], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Sage

[gaussian_binomial(n,4,-9) for n in range(4,14)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: -x^4 / ( (x-1)*(81*x-1)*(9*x+1)*(729*x+1)*(6561*x-1) ). - R. J. Mathar, Aug 03 2016