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

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

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..120

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

Programs

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

Mathematica

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

Sage

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

Formula

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