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

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

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..150

Formula

a(n) = Product_{i=1..9} ((-6)^(n-i+1)-1)/((-6)^i-1). - 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 *)

Prog

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

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

Sequence in context: A345616 A346333 A242346 * A337463 A151936 A186824

Adjacent sequences: A015375 A015376 A015377 * A015379 A015380 A015381

Keyword

sign,easy

Author

Olivier Gérard

Status

approved