A015414 Gaussian binomial coefficient [ n,11 ] for q=-9.

1, -28242953648, 897372484611991440598, -28121923404466184234811544425296, 882630281467161063728449241801432249226565, -27697404417453539188846019907159858548132165589760832, 869175534545800426775448129124238227336771807766117241522242296

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..100

Programs

Magma

r:=11; q:=-9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

Mathematica

Table[QBinomial[n, 11, -9], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

Sage

[gaussian_binomial(n,11,-9) for n in range(11,17)] # Zerinvary Lajos, May 28 2009

Formula

a(n) = Product_{i=1..11} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012