A015380 Gaussian binomial coefficient [ n,9 ] for q=-8.

1, -119304647, 16266970069380217, -2179059787976052939572615, 292539874786707389459461268654713, -39262839136506665155883080645146897495431, 5269789166381879647128952074697436662720144919161

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..130

Crossrefs

Cf. Gaussian binomial coefficients [n, 9] for q = -2..-13: A015371, A015375, A015376, A015377, A015378, A015379, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Programs

Magma

r:=9; q:=-8; [&*[(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, -8],{n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Sage

[gaussian_binomial(n,9,-8) for n in range(9,15)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..9} ((-8)^(n-i+1)-1)/((-8)^i-1). - Vincenzo Librandi, Nov 04 2012