A015376 Gaussian binomial coefficient [ n,9 ] for q=-4.

1, -209715, 58640578205, -15135778281070755, 3983313338565919030365, -1043182954580986851130914723, 273530932713230996784935699290205, -71700116580663579186545558567554787235, 18796042166858164201094703719132482337953885

Offset

9,2

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.

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 = 9..190

Formula

a(n) = Product_{i=1..9} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

G.f.: -x^9 / ( (x-1)*(16384*x+1)*(4096*x-1)*(256*x-1)*(65536*x-1)*(64*x+1)*(262144*x+1)*(4*x+1)*(16*x-1)*(1024*x+1) ). - R. J. Mathar, Sep 02 2016

Mathematica

Table[QBinomial[n, 9, -4], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 9, -4) for n in range(9, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015371, A015375, A015377,A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A233663 A232136 A183602 * A216593 A172825 A072760

Adjacent sequences: A015373 A015374 A015375 * A015377 A015378 A015379

Keyword

sign,easy

Author

Olivier Gérard

Status

approved