A015378 Gaussian binomial coefficient [ n,9 ] for q=-6.

1, -8638025, 89538572808355, -898184256176675135525, 9058617560471271225871839115, -91278255494743382265330154281509525, 919894226814090294609303909820267635374635, -9270381253910297854571803793049953719997957501525

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..150

Crossrefs

Cf. Gaussian binomial coefficients [n,9] for q = -2..-13: A015371, A015375, A015376, A015377, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Programs

Magma

r:=9; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012

Mathematica

QBinomial[Range[9,20],9,-6] (* Harvey P. Dale, Aug 16 2012 *)
Table[QBinomial[n, 9, -6],{n, 9, 18}] (* Vincenzo Librandi, Nov 04 2012 *)

Sage

[gaussian_binomial(n,9,-6) for n in range(9,16)] # Zerinvary Lajos, May 25 2009

Formula

a(n) = Product_{i=1..9} ((-6)^(n-i+1)-1)/((-6)^i-1). - Vincenzo Librandi, Nov 04 2012