A015408 Gaussian binomial coefficient [ n,11 ] for q=-4.

1, -3355443, 15011998086813, -61996192875273494691, 261050608944894743386831965, -1093857392934787687867181291059107, 4589090822384565497755014953620236474461, -19246867256860431244800698494652605702283863971

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..150

Programs

Magma

r:=11; q:=-4; [&*[(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, -4], {n, 11, 20}] (* Vincenzo Librandi, Nov 05 2012 *)

Sage

[gaussian_binomial(n,11,-4) for n in range(11,18)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..11} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - Vincenzo Librandi, Nov 05 2012