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

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

Offset

4,2

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)

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

Mathematica

Table[QBinomial[n, 4, -9], {n, 4, 20}] (* Vincenzo Librandi, Oct 28 2012 *)

Prog

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

Crossrefs

Sequence in context: A061735 A251469 A025513 * A209431 A163209 A216942

Adjacent sequences: A015292 A015293 A015294 * A015296 A015297 A015298

Keyword

nonn,easy

Author

Olivier Gérard, Dec 11 1999

Status

approved