A015407 Gaussian binomial coefficient [ n,11 ] for q=-3.

1, -132860, 26477735830, -4522934399547980, 811239619864365082573, -143119691677080990521708240, 25388050075285266699527263288120, -4495361402895546052989488899628855120

Offset: 11

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 = 11..200

Programs

Magma

r:=11; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 05 2012

Mathematica

Table[QBinomial[n, 11, -3], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Sage

[gaussian_binomial(n,11,-3) for n in range(11,19)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..11} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012