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

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

Offset: 9

Author

Olivier Gérard

Keywords

• sign
• 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 = 9..200

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

Programs

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

Mathematica

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

Sage

[gaussian_binomial(n,9,-2) for n in range(9,21)] # Zerinvary Lajos, May 25 2009

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