A015379 Gaussian binomial coefficient [ n,9 ] for q=-7.

1, -35309406, 1454546516636543, -58525570007342935110900, 2362701900656492615160524472603, -95337871447349860183019420430515900118, 3847259697771549596318959641032366290112134229

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..140

Formula

a(n) = Product_{i=1..9} ((-7)^(n-i+1)-1)/((-7)^i-1). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 9, -7], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 9, -7) for n in range(9, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; q:=-7; [&*[(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, A015378, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A250573 A210154 A216399 * A147714 A125572 A184662

Adjacent sequences: A015376 A015377 A015378 * A015380 A015381 A015382

Keyword

sign,easy

Author

Olivier Gérard

Status

approved