A015371 Gaussian binomial coefficient [ n,9 ] for q=-2.

1, -341, 232903, -105970865, 57881286463, -28735427761313, 14946527496991519, -7593183562134412385, 3902985682508407194271, -1994425683761796076272481, 1022146087305755916943130783, -523082886040328458081329117025

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..200

Formula

a(n) = Product_{i=1..9} ((-2)^(n-i+1)-1)/((-2)^i-1). - Vincenzo Librandi, Nov 04 2012

G.f.: -x^9 / ( (x-1)*(512*x+1)*(64*x-1)*(128*x+1)*(2*x+1)*(8*x+1)*(32*x+1)*(16*x-1)*(4*x-1)*(256*x-1) ). - R. J. Mathar, Sep 02 2016

Mathematica

Table[QBinomial[n, 9, -2], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 9, -2) for n in range(9, 21)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Diagonal k=9 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Cf. Gaussian binomial coefficients [n,9] for q=-2..-13: A015375, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A309285 A317556 A006107 * A328665 A163582 A239271

Adjacent sequences: A015368 A015369 A015370 * A015372 A015373 A015374

Keyword

sign,easy

Author

Olivier Gérard

Status

approved