A015381 Gaussian binomial coefficient [ n,9 ] for q=-9.

1, -348678440, 136773736379522605, -52916360230556551635386480, 20504007291105533368839949866598015, -7943538006665671364765186721016327317109448, 3077495169782617972230910362141435994555138110002155

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..120

Formula

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

Mathematica

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

Prog

(Sage) [gaussian_binomial(n, 9, -9) for n in range(9, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; q:=-9; [&*[(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, A015379, A015380, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A316745 A351459 A358705 * A257384 A186628 A032757

Adjacent sequences: A015378 A015379 A015380 * A015382 A015383 A015384

Keyword

sign,easy

Author

Olivier Gérard

Status

approved